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MECHANICAL DRAWING 

A PRACTICAL MANUAL OF SELF-INSTRUCTION IN THE ART 
OF DRAFTING, LETTERING, AND REPRODUCING 
PLANS AND WORKING DRAWINGS, WITH 
ABUNDANT EXERCISES AND PLATES 


BY 

ERVIN KENISON, S. B. 

>i 

ASSOCIATE PROFESSOR OF DRAWING AND DESCRIPTIVE GEOMETRY, 
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 

REVISED BY 

^.yfcr . . 

EDWARD B. WAITE 

FORMERLY DEAN AND HEAD CONSULTING DEPARTMENT, AMERICAN SCHOOL OF 
CORRESPONDENCE, AMERICAN SOCIETY OF MECHANICAL ENGINEERS 


- > 

ILLUSTRATED 


AMERICAN TECHNICAL SOCIETY 
CHICAGO 
1917 




v 



COPYRIGHT, 1913 , 1917 , BY 
AMERICAN TECHNICAL SOCIETY 


COPYRIGHTED IN GREAT BRITAIN 
ALL RIGHTS RESERVED 


MAY - 5491 ? 

©CI.A462277 
“I'M) ( , 





INTRODUCTION 


A TRAINED architect or architectural draftsman will execute a 
set of plans for a house or flat building with a dispatch and 
precision which is a delight to anyone sufficiently acquainted 
with these details to appreciate the ability shown. The knowledge 
of the conventions used, the accuracy of scale, the methods of 
representing this or that detail of construction show a wonderful 
facility of execution and broad acquaintance with such work. Like¬ 
wise, the structural or the machine draftsman, with the same 
precision and with no mean engineering ability and inventive skill, 
will draw the complete details for a bridge truss, a steel frame of 
an office building, or a complicated machine. He will give just 
the information necessary for the steel fabricator, for the contractor 
on the work, for the pattern maker, and for the shop man. 

<1 All of these details represent advanced processes in architectural 
and engineering drafting. And yet, these same men who show 
such skill had to acquire their training through careful and pains¬ 
taking study and practice of the rudiments of mechanical drawing. 
They had first to lay their foundation for the more advanced work 
by learning the kind of equipment necessary for drawings of 
various kinds, the use of the T-square, the triangles, the ruling 
pen, and all the other instruments which must be used from time 
to time. They had to train their eyes to visualize objects and 
measure distances, and their hands to draw, with precision, lines of 
uniform width and accurate direction. They had to learn the 
rules of geometrical construction; the methods of representing 
plans and elevations of objects; and the principles of orthographic 
and isometric projection and profile work. 

<§ All of these important features are carefully treated in this 
work; the studies are illustrated by diagrams and plates, and the 
student is carried from the simplest drawing problems to those 
which, in difficulty, border on the architectural and engineering 
fields. It is the hope of the publishers that the book will be found 
a useful addition to engineering literature. 






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SECTIONAL ELEVATION OF NEW CROSSLEY OIL ENGINE 

Courtesy of Crossley Brothers , Manchester , England 









































































































































































CONTENTS 

DRAWING METHODS 

PAGE 

Instruments and materials. 1 

Drawing paper. j 

Drawing board. 2 

Thumb tacks. 3 

Pencils. 3 

Erasers. 4 

T-square. 4 

Triangles. g 

Compasses. 10 

Dividers. 12 

Bow pen and pencil. 13 

Drawing pen. 13 

Ink. 14 

Scales. 15 

Protractor.. 15 

Irregular curve. 16 

Beam compasses. 16 

Lettering. 17 

Forming. 17 

Spacing. 18 

Inking. 18 

Style. 19 

Preliminary line problems. 26 

Penciling. 27 

Inking. 27 

Instructions. 22 

How to hold instruments. 22 

“Don’ts” in drafting work. 25 

Examination plates.29-38 

GEOMETRICAL DEFINITIONS 

Lines. 41 

j Surfaces. 42 

; Triangles. 43 

Quadrilateral's. 44 

Measurement of angles. 46 

Solids. 47 

Prisms. 47 

Pyramids. 48 

Conic sections. 51 

Ellipse. 51 

Parabola.. • 52 

Hyperbola. 52 

Rectangular hyperbola. 53 














































CONTENTS 


Odontoidal curves. 

Cycloidal curves 
Involute curves. 


PAGE 

. 53 
. 53 
. 54 


GEOMETRICAL PROBLEMS 


To bisect a given straight line. 

To construct an angle equal to a given angle. 

To draw through a given point a line parallel to a given line.. .. 

To draw a perpendicular to a line from a point without the line. 

To bisect a given angle. 

To divide a line into any number of equal parts. 

To construct a triangle having given the three sides. 

To construct a triangle having given one side and the two adjacent angles.. .. 
To inscribe an arc or circumference through three given points not in the 

same straight line... 

To inscribe a circle in a given triangle. 

To inscribe a regular pentagon in a given circle. 

To inscribe a regular hexagon within a given circle. 

To draw a line tangent to a circle at a given point on the circumference.... 

To draw a line tangent to a circle from a point outside the circle. 

To draw an ellipse when the axes are given. 

To draw an ellipse by means of a trammel. 

To draw a spiral of one turn in a circle. 

To draw a parabola when the abscissa and ordinate are given. 

To draw a hyperbola when the abscissa, the ordinate, and the diameter are 

given. 

To construct a cycloid when the diameter of the generating circle is given. 

To construct an epicycloid when the diameter of the generating circle and the 

diameter of the director circle are given. 

To draw a hypocycloid when the diameter of the generating circle and the 

radius of the director circle are given. 

To draw the involute of a circle when the diameter of the base circle is known. 


55 

57 

59 

59 

61 

61 

61 

62 

62 

62 

64 


65 

67 

67 

67 


67 

68 

70 

70 

71 


PROJECTIONS 


Orthographic projection. 73 

Definitions. 73 

Projection methods. 76 

Drawing the projection on paper. 79 

Ground line. 80 

Rules of projection. 81 

Typical examples of projection. 82 

Principles. 87 

True length by revolving vertical projection. 88 

Rectangular prism or block. 89 

Triangular prism or block. 89 

Triangular block with square hole. 90 







































CONTENTS 


PAGE 

Rotating and inclining of objects. 90 


Pyramid. 91 

Cylinder in inclined position to horizontal plane. 92 

Cylinder greatly inclined to horizontal plane. 95 

Planes with planes. 98 

Planes with cones or cylinders. 103 

Development of surfaces. 106 

General details of process. 106 

Right cylinder. 107 

Right cone. 108 

Rectangular prism. 108 

Cone. 109 

Regular triangular pyramid. 110 

Truncated circular cylinder. Ill 

Isometric projection. 113 

Isometric of a cube. 113 

Applications of isometric projections. 116 

Characteristics of various isometrics. 116 

Oblique projection. 123 

Comparison with isometric projection. 123 

Characteristics of method. 123 


MISCELLANEOUS METHODS 


Line Shading. 126 

Object of line shading. 126 

Lettering. 128 

Types of lettering. 128 

Size of letters. 128 

Penciling before inking. 133 

Titles for working drawings. 133 

Plates. 134 






































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MECHANICAL DRAWING 


PART I 


The subject of mechanical drawing is of great interest and 
importance to all mechanics and engineers. Drawing is a method 
of showing graphically the minute details of machinery; it is the 
language by which the designer speaks to the workman; it is the most 
graphical way of placing ideas and calculation on record. A brief 
inspection of an accurate, well-executed working drawing gives a 
better idea of a machine than a lengthy written or verbal description. 
The better and more clearly a drawing is made, the more intelligently 
the workman can comprehend the ideas of the designer. Thorough 
training in this important subject is necessary to the success of every¬ 
one engaged in mechanical work. 

The draftsman is dependent for his success, to a certain extent, 
upon the quality of the instruments and materials which he uses. 
As a beginner, he will find a cheap grade of instrument sufficient 
for his needs; but after he has become expert, it will be necessary for 
him to procure those of better construction and finish to enable him 
to do accurate work. It is a better plan to purchase the well-made 
instruments, if possible, at the start. 

INSTRUMENTS AND MATERIALS 

Drawing Paper. In selecting drawing paper, > the first thing 
to be considered is the kind of paper most suitable for the proposed 
work. For shop drawings, a manila paper is frequently used on 
account of its toughness and strength, for these drawings are likely 
to be subjected to considerable hard usage. If a finished drawing 
is to be made, the best white drawing paper should be obtained, so 
that the drawing will not fade or become discolored with age. A 
good drawing paper should be strong; should have uniform thick¬ 
ness and surface; should stretch evenly and lie smoothly when stretched 




2 


MECHANICAL DRAWING 


or when ink or colors are used; should neither repel nor absorb liquids; 
and should allow considerable erasing without spoiling the surface. 
It is, of course, impossible to find all of these qualities in any one ' 
paper, as great strength cannot be combined with fine surface. How¬ 
ever, a kind should be chosen which combines the greatest number 
of these qualities for the given work. Of the higher grades of papers, j 
Whatman’s are considered by far the best. This paper, either side 
of which may be used, is made in three grades: the hot pressed, which 
has a smooth surface and is especially adapted for pencil and very 
fine line drawing; the cold pressed, which is rougher than the hot 
pressed, has a finely grained surface, and is more suitable for water 
color drawing; and the rough, which is used for tinting. For general 
work, the cold pressed is the best as erasures do not show as plainly 
on it, but it does not take ink as well as the hot pressed. 

Whatman’s paper comes in sheets of standard sizes as follows: 


Cap. 13X17 inches Imperial . . . . 22x30 inches 

Demy. 15x20 “ Atlas. 26X34 “ 

Medium. 17X11 “ Double Elephant . . 27x40 “ 

Royal . ... 19X24 Antiquarian . . . 31X53 “ 

Super-Royal ... 19x27 “ 


The usual method of fastening paper to a drawing board is by 
means of thumb tacks or small one-ounce copper or iron tacks. 
First fasten the upper left-hand corner and then the lower right, 
pulling the paper taut. The other two corners are then fastened, 
and a sufficient number of tacks placed along the edges to make the 
paper lie smoothly. For very fine work, however, it is better to stretch 
the paper and glue it to the board. Turn up the edges of the paper 
all the way round—the margin being at least one inch—then moisten 
the surface of the paper by means of a sponge or soft cloth, and spread 
paste or glue on the turned-up edges. After removing all the surplus 
water on the paper, press the edges down on the board, commencing 
at one corner and stretching the paper slightly —if stretched too 
much it is liable to split in drying. Place the drawing board in a 
horizontal position until the paper is dry, when it will be found to be 
as smooth and tight as a drum head. 

Drawing Board. The drawing board, Fig. 1, is usually made of 
well-seasoned and straight-grained soft pine, the grain running 
lengthwise of the board. Each end of the board is protected by a 







MECHANICAL DRAWING 


3 


side strip— If to 2 inches in width—whose edge is made perfectly 
straight for accuracy in using the T-square. Frequently the end 



pieces are fastened by a glued matched joint, nails or screws. Two 
cleats on the bottom, extending the whole width of the board, will 
reduce the tendency to warp. Drawing boards are made in sizes to 
accommodate the sizes of paper in general use. 

Thumb Tacks. Thumb tacks are used to fasten the paper to 
the drawing board. They are usually made of steel, pressed into 
shape—as in the cheaper grades—or with heads of German silver, the 
points being screwed and riveted to them. For most work, drafts¬ 
men use small one-ounce copper or iron tacks, as they are cheap and 
can be forced flush with the drawing-paper, thus offering no obstruc¬ 
tion to the T-square. 

PencilSo Lead pencils are graded according to their hardness, 
the degree of which is indicated by the letter H—as HH, 4H, 6H, 
etc. For general use a lead pencil of 5H or 6H should be used, 
although a softer 4TI pencil is better for making letters, figures, and 
points. The hard lead pencil should be.sharpened as shown in 
Fig. 2 so that in penciling a drawing the lines may be made very fine 
and light. The wood is cut away so that about f or ^ inch of lead 





















4 


MECHANICAL DRAWING 


projects. The lead can then be sharpened to a chisel edge by nibbing 
it against a bit of sand paper or a fine file, and the corners slightly , 
rounded. In drawing the lines the draftsman should place the chisel 
edge against the T-square or triangle, thus 
enabling him to draw a fine line exactly 
through a given point. If the drawing is not 
to be inked, but is made for tracing or for 
rough usage in the shop, a softer pencil, 3H 
or 4H, may be used, so as to make the lines j 
somewhat thicker and heavier. The lead for j 
compasses may also be sharpened to a point 
although some draftsmen prefer to use a chisel 
edge for the compasses as well as the pencil. 

In using a very hard lead pencil a light pres- : 
sure should be used as otherwise the chisel 
edge will make a deep impression in the paper 
which cannot be erased. 

Erasers. What little erasing is necessary in making drawings, 1 
should be done with a soft rubber. To avoid erasing the surrounding '* 
work some draftsmen use a card in which a slit is cut about 3 inches 

I (<=> 2 

c==j 0 ° 

_I V c 3 J 

Fig. 3. Erasing Shield Fig. 4. Metal Erasing Shield 

long and J to i inch wide, Fig. 3. An erasing shield of thin metal, 
Fig. 4, is also very convenient, especially in erasing letters. For 
cleaning drawings when they are completed, a sponge rubber or a 
preparation called "art gum’ , may be used, but in either case care 
should be taken not to make the lines dull by too hard rubbing. 

T=Square. The T-square, which gets its name from its general 
shape, consists of a thin straight-edge, the blade , with a short piece, 
the head , fastened at right angles to it, Fig. 5. T-squares are usually 
made of wood, the pear and maple woods being used in the cheaper 
grades, and the harder woods, like mahogany, with protecting edges 



Fig. 2. Pencil Sharpened 
to a Chisel Point 



















MECHANICAL DRAWING 


5 


or ebony or celluloid, Fig. 6, in the more expensive instruments. 
The head is designed to fit against the edge of the drawing board, 
allowing the blade to extend across the surface of the board. It is 



Fig. 5. Common T-Square 


desirable to have the blade of the T-square make a right angle with 
the head, but this is not absolutely necessary, if the head is always 
placed against the left-hand edge of the board, for the lines drawn 



Fig. 6. Mahogany-Bound T-Square 

with the T-square will then be referred to one edge of the board only, 
and if this edge is straight, the lines will be parallel to each other. 

T-squares are sometimes provided with swiveled heads as it is 
frequently very convenient to draw lines parallel to each other which 
are not at right angles to 
the left-hand edge of the 
board. To use the T- 
square in drawing parallel 
horizontal lines,* place the 
head of the T-square in 
contact with the left-hand 
edge of the board. Fig. 7, 
and draw the pencil along 
the upper edge of the 
blade at each new posi¬ 
tion of the T-square. Only the upper edge should be used as the 


Fig. 7. Drawing Parallel Lines 


* See page 23. 


























6 


MECHANICAL DRAWING 


two edges may not be exactly parallel and straight. In trimming 
drawings or cutting the paper from the board, always use the lower, 
edge of the T-square so that the upper edge may not be made untrue. 

For accurate work it is absolutely necessary that the upper edge 
of the T-square be exactly straight. To test the straightness of the 

edge two T-squares may be 
placed together as shown in 
Fig. 8. However, a lack of contact 
such as show T n in the figure does 
not prove which edge is crooked, 
and for this determination a third 
blade must be used and tried 
with the two given T-squares successively. 

Triangles. Triangles are made of various substances such as 
wood, rubber, celluloid, and steel. Wooden triangles are cheap but 
are likely to warp out of shape; rubber triangles are frequently used, 
and are, in general, satisfactory; celluloid triangles are extensively 
used on account of their transparency, which enables the draftsmen 



In using a rubber or celluloid triangle take care that it lies perfectly 
flat and is hung up when not in use; when allowed to lie on the draw¬ 
ing board with a pencil or an eraser under one corner it will become 
warped in a short time, especially if the room is hot or the sun happens 
to strike the triangle 

Triangles fiom 6 to 8 inches on a side will be found convenient 
for most work, although there are many cases where a small triangle 



Fig. 8. Testing the Edge of T-Square 



















MECHANICAL DRAWING 


7 


measuring about 4 inches on a side will be found useful. Every 
draftsman should have at least two triangles, one having two angles 
of 45 degrees and one right angle; and the other having angles of 
30, 60, and 90 degrees, respectively, Fig. 9. 

The value of the triangle depends upon the accuracy of the 
angles and the straightness of the edges. To test the accuracy of 


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Fig. 10. Testing a Right Angle (45° Triangle) 


the right angle of a triangle, place the triangle with the lower edge 
resting on the T-square in position A, Fig. 10. Now draw the line 
C D, which, if the triangle be true, will be perpendicular to the edge 
of the T-square. Transfer the triangle to position B, and if the right 
angle of the triangle is exactly 90 degrees the left-hand edge of the 
triangle will exactly coincide with the line C D. 

To test the accuracy of the 45-degree angles place the triangle 
with the lower edge resting on the working edge of the T-square, 


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Fig. 11. Testing 45° Angle (45° Triangle) 


and draw the line E F, Fig. 11. Now without moving the T-square 
place the triangle so that the other 45-degree angle is in the position 
occupied by the first. If the two 45-degree angles coincide they are 
accurate. 



































8 


MECHANICAL DRAWING 


Triangles are used in drawing lines at right angles to the T- 
square, Fig. 12, and at an angle with the horizontal, Fig. 13. If it is de¬ 
sired to draw a line through the point P, Fig. 14, parallel to a given 


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Fig. 12. Drawing Vertical Parallel Lines 


line E F , two triangles should be used. First, place triangle A with 
one edge coinciding with the given line. Now take triangle B and 
place one of its edges in contact with the bottom edge of triangle A. 
Holding triangle B firmly with the left hand, slide triangle A to the 
right or to the left until its edge reaches the point P. The line M N 
may then be drawn passing through the point P. In place of the 
triangle B any straight-edge such as a T-square may be used. 



Fig. 13. Drawing Parallel Lines at an Angle with the Horizontal 

A line may be drawn through a point, perpendicular to a given 
line by means of triangles as follows: Let E F, Fig. 15, be the mven 
line, and let the point be D. Place the longest side of triangle A so 
that it coincides with the line E F. Place the other triangle (or any 
straight-edge) in the position of the triangle B; then holding B with 
the left hand, place the triangle A in the position C, so that the longest 
side passes through the point D. A line may then be drawn through 
the point D perpendicular to E P. 






































MECHANICAL DRAWING 


9 


In previous figures it has been shown how lines may be drawn 
making angles of 30, 45, 60, and 90 degrees with the horizontal. 



Fig. 14. Drawing a Line Parallel to a Fig. 15. Drawing a Line Perpendicular 
Given Line to a Given Line 


It is possible to draw lines forming angles of 15 and 75 degrees by 
placing the triangles as shown in Fig. 16. 



Fig. 16. Drawing Angle of 15° and 75° 


By the use of the triangles and T-square almost any line may be 
drawn. Suppose it is desired to draw a rectangle having one side 






o 

\ 

Q 

1 \ 

\ 

\ 

IVx 

/?---' X 

- X 


o o 


o 



o ° 





Fig. 17. Drawing a Rectangle with T-Square and Triangle 

horizontal. First draw by means of the T-square the sides A B 
and D C horizontal and parallel, Fig. 17. Now place one of the 




















































10 


MECHANICAL DRAWING 


triangles on the T-square and in positions E and F draw the vertical 
lines D A and B C. 

If the rectangle is to be 
drawn in some other position 
on the board, as shown in Fig. 

18, place the 45-degree triangle 
F so that the longest edge is in 
the required direction of the side 
D C. Now, hold the triangle F 
in position and place another 
triangle in position H. By hold- 



Fig. 18. Rectangle Drawn with Triangles 




ing H in position and sliding triangle F, the sides A B and D C 
may be drawn. To draw the sides A D and B C change triangle 
F to position E and repeat the process. 

Compasses. Compasses are used for 
drawing circles and arcs of circles. The 
cheaper class of instruments are made of 
brass, but they are unsatisfactory on 
account of the odor and the tendency to 
tarnish. The best material is German 
silver, as it does not soil the hands, has 
no odor, and is easy to keep clean. 
Aluminum instruments possess the ad¬ 
vantage of lightness, but on account of 
the softness of the metal they do not 
wear well. 

The compasses are made in the form 
shown in Fig. 19 and are provided with 
pencil and pen points. Fig. 20 shows 
the compass in position for drawing circles. 
One leg has a socket into which the 
shank of the pencil or pen mounting may 
be inserted. The other leg is fitted with 
a needle point which is placed at the 
center of the circle. In most instruments 
the needle point projects through a piece 
of round steel wire with a square shoulder at one or both ends. 
In some instruments the joints are held in position by lock nuts, 


Fig. 19. Compasses and 
Attachments 



























MECHANICAL DRAWING 


11 


made of thin disks of steel, with notches for using a wrench or forked 
key. big. 21 shows the detail of the joint of a high grade instrument. 

Both legs are alike at the joint, 
and two pivoted screws are inserted 
in the yoke. This permits ample 
movement of the legs, yet gives 
the proper stiffness. The flat sur¬ 
face of one leg is faced with steel, 
the other with German silver, so 
that the rubbing parts may be of 
different metals. Small set screws 
are used to prevent the pivoted 
screws from turning in the yoke. 
The contact surfaces of this joint 
are made circular to exclude dirt 
and to prevent rusting of the 
steel face. 

The details of the socket are 
shown in Fig. 22, Fig. 23, and 
Fig. 24; in some instruments the 
shank and socket are pentagonal, 
Fig. 22, the shank entering the 
Fig. 20. Compasses Set for Drawing Circles socket loosely, and being held 
in place by means of the screw. Unless used very carefully this 
arrangement is not durable be¬ 
cause the sharp corners soon wear, 
and the pressure on the set screw 
is not sufficient to hold the shank 
firmly in place. 

In Fig. 23 is shown a round 
shank, the shank having a flat 
top, with a set screw to hold the 
shank in position. A still better 
form of socket is shown in Fig. 24 ? 
the hole being circular and taper¬ 
ed. The shank fits accurately into the split socket and is clamped by 
a screw on the side; it is held in perfect alignment by a small steel key. 

Both legs of the compass are jointed in order that the lower part 





Details of Compass Joint 

















12 


MECHANICAL DRAWING 


of the legs may be perpendicular to the paper while drawing circles. 
In this way the needle point makes but a small hole in the paper, 
and both nibs of the pen will press equally on the paper. In penciling 
circles it is not as necessary that the pencil should be kept vertical; 




Fig. 22. Pentagonal Shank and Socket 


Fig. 23. Circular Shank and Socket 


it is a good plan, however, to learn to use them in this way both in 
penciling and inking. The compasses should be held loosely be¬ 
tween the thumb and forefinger. If the needle point is sharp, as it 

should be, only a slight pressure will be 
required to keep it in place. While 
Fig. 24. Circuiar^Sockct with drawing the circle, incline the compasses 
slightly in the direction of revolution 
and press lightly on the pencil or pen. 

In removing the pencil or pen attachment from the com¬ 
pass it should be pulled out straight in order to avoid enlarg¬ 
ing the socket, and thus rendering the instrument inaccurate. 
For drawing large circles use the lengthening bar, Fig. 19, 
steadying the needle point with one hand and describing 
the circle with the other. 

Dividers. Dividers, which are similar to compasses, are 
used to lay off distances on the drawing, either from a scale or 
from other parts of the drawing, Fig. 25. They are also 
used for dividing a line into equal parts. To do this turn 
the dividers in the opposite direction each time, Le., move 
the point alternately to the right and to the left. The points 
of the dividers should be very sharp so that the holes made 
in the paper will be small, thus assuring accurate spacing. 
Compasses may be used as dividers by substituting for the 
pencil or pen point an extra steel point, usually furnished 
with the instrument. In place of dividers many drafts¬ 
men use a needle point. The needle, with the eye-end broken 
off, is forced into a handle of soft pine, making a con- 
r venient instrument for marking line intersections and 
Dividers distances. 






















MECHANICAL DRAWING 


13 


Bow Pen and Bow Pencil. Ordinary large compasses are too 
heavy and the leverage of the long leg is too great to allow small circles 
to be drawn accurately. For this reason the bow compasses, Figs. 
26 and 27, should be used on all arcs and circles having a radius of 
less than f inch, such as those which represent boiler tubes and bolt 



Fig. 26. Bow Pencil 



Fig. 27. Bow Pen 


Fig. 28. Bow Divider 



holes. When small circles are drawn, the needle point must be 
adjusted to the same length as the pen or pencil point. If a con¬ 
siderable change in radius is made, press the points together before 
turning the nut so as to prevent wear in the screw threads. The 
bow dividers. Fig. 28, replace the ordinary dividers in small work 
and have the advantage of a fixed adjustment. 

Drawing Pen.* For drawing straight lines and curves that are 
not arcs of circles, the line pen—sometimes called the ruling pen—is 



Fig. 29. Drawing Pen 

used, Fig. 29. The distance between the pen points, which regulates 
the width of line to be drawn, is adjusted by the thumb screw, and 
the blades are given a slight curvature so that there will be a cavity 
for ink when the points are close together. 


*See page 22. 








14 


MECHANICAL DRAWING 


The pen should not be dipped in the ink but should be filled by 
means of a common steel pen or quill, to a height of about \ or | 
inch; if too much ink is placed in the pen it is likely to drop out and 
spoil the drawing. Upon finishing the work wipe the pen with 
chamois or a soft cloth, because most liquid inks corrode the steel. 

In using the pen, care should be taken that both blades bear 
equally on the paper, in order that the line may be smooth. The pen | 
is usually inclined slightly in the direction in which the line is drawn 
and should touch the triangle or T-square lightly so as not to press 
the blades together and thereby change the width of the line; the 
pen must not be tipped outward, however, as the danger of blotting 
is greatly increased when the line is drawn so close to the guide. • 

Sharpening the Drawing Pen. When it is impossible to make 
a smooth line with the drawing pen, it should be sharpened. Screw 
the blades together and grind them to a parabolic shape by drawing 
the pen back and forth over a small, flat, close-grained oilstone. 
This process, of course, makes the blades dull but insures their being 
of the same length. Now separate the points slightly and rub one 
of them on the oilstone, keeping the pen at an angle of from 10° to 15° 
with the face of the stone, and giving it a slight twisting movement. 
This part of the operation requires great care as the shape of the ends 
must not be altered. After one point has become fairly sharp, grind 
the other in a similar manner, grinding always on the outside of the 
blades and removing the burr from the inside with leather or pine 
wood. Test the pen by filling with ink and drawing several lines. 
Unless the lines are smooth, the grinding must be continued. 

Ink. India ink is always used for drawing as it makes a per¬ 
manent black line; it is obtainable in solid stick or liquid form. The 
liquid form is much more convenient but contains acid which cor- 1 
rodes steel and makes it necessary to keep the pen perfectly clean. 

To prepare the ink in stick form for use, put a little water in a 
saucer and place one end of the stick in it; then by a twisting motion 
grind enough ink to make the water black and slightly thickened. 
Now draw a heavy line on a sheet of paper and if after drying the line 
has a grayish appearance, more grinding is necessary. Wipe the 
stick dry after using to prevent crumbling. It is well to grind the 
ink in small quantities as it does not dissolve readily a second time; 
however, if covered it will keep for two or three days. 




MECHANICAL DRAWING 


15 


Scales, The scales used for obtaining measurements on draw¬ 
ings are made in several forms, the most convenient being the flat , 
with beveled edges, and the triangular. The scale is usually graduated 
for a distance of 12 inches. The triangular scale, Fig. 30, has six 



Fig. 30. Triangular Scale 


surfaces for different graduations, and the scales are arranged so that 
the drawings may be made in any proportion to the actual size. For 
mechanical work, the common divisions are multiples of two; thus 
drawings are made full size, \ size, J, J, Vt* etc- If a drawing 

is \ size, 3 inches equals 1 foot, hence 3 inches is divided into 12 equal 
parts and each division represents one inch. If the smallest division 
on a scale represents inch, the scale is said to read to jV inch. 

Scales are often divided into T V, -gV, etc., f° r architects 
and civil engineers, and for measuring indicator cards. 

The scale should never be used as a substitute for the triangle or 
T-square in drawing lines. 

Protractor. The protractor, an instrument used for laying off 
and measuring angles, is made of steel, brass, horn, or paper. When 



made of metal the central portion is cut out, Fig. 31, so that the drafts¬ 
man may see the drawing. The outer edge is divided into degrees 

















16 


MECHANICAL DRAWING 


and tenths of degrees. To lay off the required angle—use a very 
sharp, hard pencil in order that the measurements may be accurate— 
place the protractor so that the two zero marks are on the given line, 
produced, if necessary, and the center of the circle is at the point 
through which the desired line is to be drawn. 

Irregular Curve. One of the conveniences of a draftsman’s 
outfit is the French or irregular curve , which is used for drawing curves 
other than arcs of circles, with either pencil or line pen. This instru¬ 
ment, which is made of wood, hard rubber, or celluloid—celluloid 
being the best—is made in various shapes, one of the most common 
being shown in Fig. 32. Curves drawn with an irregular curve 
are called free hand curves. 

To draw a curve through a series of located points find that 
position of the irregular curve that passes through three points, 



say, and draw the line through them, Fig. 33. Now shift the curve 
so as to include a part of the curve already drawn and two or three 
more points. Draw the curve through these points, continuing 
this process until the curve is completed. If, at each new setting, 
the line is not carried quite as far as the coincidence of the irregular 
curve would permit, a smoother curve will result. It frequently 
facilitates the work and improves its appearance to draw a pencil 
curve free hand through the points and then use the irregular curve, 
taking care that it always fits at least three points. In inking the 
curve, the blades of the pen must be kept tangent to the curve. 
For certain kinds of work, irregular curves of plastic metal are some¬ 
times used to fit exceptionally erratic curves. 

Beam Compasses. The ordinary compasses are suitable for 
drawing circles up to 8 or 10 inches diameter. For larger circles 
beam compasses are provided. The two parts called channels 






MECHANICAL DRAWING 


17 


which carry the pen or pencil and the needle point are clamped to a 
wooden beam at a distance equal to the radius of the circle. The 



Fig. 33. Channels of Beam Compass 


chumb nut underneath one of the channel pieces makes accurate 
adjustment possible. 

LETTERING 

No mechanical drawing is finished unless all headings, titles, 
and dimensions are lettered in plain, neat type. Many drawings 
are accurate, well-planned, and finely executed but do not present 
a good appearance because the draftsman did not think it worth 
while to letter carefully. Lettering requires time and patience 
especially for the beginner; and many think it a good plan to practice 
lettering before commencing drawing. Poor writing need not neces¬ 
sarily mean poor lettering, for good writers do not always letter well. 

In making large letters for titles and headings it is often neces¬ 
sary to use drawing instruments and mechanical aids, but small 
letters, such as those used for dimensions, names of materials, dates, 
etc., should be made free=hand. 

Forming. The student is apt to think that, lettering is a form 
of mechanical drawing, that the use of the straight-edge is the prin¬ 
cipal operation, and that letters, forms, and the spaces between are 
to be figured out by measurement. On the contrary, lettering is 
design, and the draftsman so distributes the letters in the spaces 
arranged for them as to make a combination that will be pleasing 
to the eye. The requirements for a good design are simplicity and 
uniformity. These are acquired by accuracy in detail and by good 
judgment and taste, as no practical rules can be followed which will 





18 


MECHANICAL DRAWING 


invariably produce the same result. Letter forms are, to a certaii 
extent, standard. The lettering for a title is usually done very care 
fully and accurately, while practically all of the other lettering on t 
drawing is done rapidly and in a simple style. To develop a lettej 
use the same method of procedure as in drawing a straight line betweerj 
two points. First, draw the guide lines rather carefully and therj 
block out the general form of the letter by a series of short stroked 
of the pencil. Continue this method, straightening the lines anc! 
rounding the curves of the latter until its form is satisfactory. 

Spacing. The spacing of the letters is very important and is 
best obtained by the unaided eye just as are the proportions of the 
letters. Care must be taken to allow a clear distance between letters j 
the space varying according to the combination. For instance, sue! 
letters as A, V, and W spread more at one part than at another anc 
therefore do not fill the space completely. Of course, when the 
distance between letters is large any such irregularities will not be 
noticeable. The best method for obtaining good space values is b\j 
sketching in the letters roughly and then bringing them to a good 
appearance by correction and adjustment The first results are, ol 
course, unsatisfactory, but after the eye and hand have become 
trained, great improvement will be noticed. A simple aid to this 
development will be found in the use of a piece of cardboard with 
the widths of the enclosing rectangles or parallelograms of the differ¬ 
ent letters marked on its edge, by which the spacing made by the eye 
may be checked. 

Inking. In practical work most of the lettering is penciled in 
and then finished in ink. As faults in letters which may not be 
noticed in the penciled work stand out clearly after inking, it is not 
advisable to ink in the penciled letter accurately, but rather to im¬ 
prove upon it. 

For lettering free-hand, use a pen that will make the full weight 
of line desired without much pressure, holding it squarely on the 
paper and directly in front. A new pen, which is apt to give too fine 
a line, may be remedied by scratching a little on a rough surface. 
If a pen is kept clean and all hardened ink removed so that the nibs 
are not spread, the pen wdll last a long time. A coarser pen must be 
used on rough than on smooth paper. 

To remove a faulty line or a blot, let the ink dry thoroughly, 




MECHANICAL DRAWING 


19 


then with a sand rubber, erase the spot carefully, rubbing around it, 
as well. Clean the sand out of the surface with a pencil eraser 
iiand finally polish down with a piece of ivory or smooth wood. Pencil 
1 in the parts erased as if doing the work for the first time and again 
1 ink in, using special care, as the ink is more likely to spread on an 
1 erased surface than anywhere else. 

Style. There are many styles of letters used by draftsmen, but 
almost any neat letter free from ornamentation is acceptable in 
regular practice. For titles, large Roman capitals are preferred, 

: although Gothic and black letters also look well and are much easier 
■ to make. The vertical and inclined or italicized Gothic capitals 
i shown in Fig. 34 and Fig. 35, are neat, plain, and easily made. This 

UPRIGHT GOTHIC 


©HnnsHSHi 


QKIUMKtnHOH 


iHsaHHiaraHn 


Fig. 34. Upright Gothic Capitals 


latter style possesses the advantage over the vertical type in that a 
slight difference in inclination is not apparent. 

The curves of the inclined Gothic letters such as those in B, C , 
G, J, etc., are somewhat difficult to make free-hand, especially if the 
letters are about one-half inch high. In the alphabet, Fig. 36, the 
letters are made almost wholly of straight lines, the corners only 
being curved. 

The first few plates of this work will require no titles, the only 
lettering being the student’s name, the date, and the plate number 























































20 


MECHANICAL DRAWING 


which will be done in inclined Gothic capitals. Later the subject or 
lettering will again be taken up in connection with titles and headings- 
for drawings which show the details of machines. 

To make the inclined Gothic letters, first draw two parallel lines 
A inch apart to mark the height for the letters of the date, name-, 

ABCDETGH/J 
KL MNOBQH 
STUVWXYZ 

Fig. 35. Inclined Gothic Capitals 

and plate number. This is the height to be used on all plates through¬ 
out this work, unless other directions are given. When two sizes of 
letters are used, the smaller should be about two-thirds as high as 6 
the larger. The inclination of the letters should be the same for all, ! 

BCBErGHUKL M 
NOPQR S TU VWX YZ 
/B 3-45G7890 

Fig. 36. Inclined Gothic Capitals— Straight Lines with Curved Corners 

and as an aid to the beginner, light pencil lines may be drawn 
about J inch apart, forming the proper angle with the parallel lines 
already drawn; this angle is usually about 70°, but if a 60° triangle 
is at hand, it may be used in connection with the T-square as shown 
in Fig. 38. 

Capital letters such as D, E, F, L, Z, etc., should have their 
top and bottom lines coincide with the horizontal guide lines, as other¬ 
wise the work will look uneven. Letters, of which C, G, 0, and 0 
are types, may be formed of curved or straight lines. If made o* 





MECHANICAL DRAWING 


21 


curved lines, their height should be a little greater than the guide 
lines to prevent their appearing smaller than the other letters. In 
this work they may be made of straight lines with rounded corners 
;as such letters are easily constructed and may be made of standard 
height. 

To construct the letter A, use one of the 60° lines as a center line. 
Then from its intersection with the upper horizontal line drop a 
perpendicular to the lower guide line. Draw another. line from 
the vertex meeting the lower guide line at the same distance on the 
other side of the center line. The cross line of the A should be a little 
below the center. The V is an inverted A without the cross line. 
For the letter M, the side lines should be parallel and about the same 
distance apart as the guide lines. The side lines of the W are not 
parallel but are farther apart at the top. The J is not quite as wide 
as such letters as II, E, N, R, etc. To make a Y, use the same 
spread as in making a V but let the diverging lines meet the center 
line a little below the middle. 

The lower-case letters are shown in Fig. 37. In such letters 


abcc/efgh/jk/mn 
opqrs tuvwjcyz 


Fig. 37. Inclined Gothic Lower-Case Letters 


as m, n, r, etc., make the corners slightly rounding. The letters 
a, b, c, e, g, o, p , q, should be full and rounding. 

The style of the Arabic numerals is given in Fig. 36; Roman 
numerals are made of straight lines. 

At first the copy should be followed closely and the letters drawn 
in pencil; the inclined guide lines may be used until the proper in¬ 
clination becomes firmly fixed in mind when they should be aban¬ 
doned. The horizontal lines, however, are used at all times by 
most draftsmen. After considerable practice has been had the 
letters may be constructed in ink without first using the pencil. 
When proficiency has been attained in the simple inclined Gothic 
capitals, the vertical, block and Roman alphabets should be studied. 





22 


MECHANICAL DRAWING 


HOW TO HOLD DRAWING INSTRUMENTS 

Position of Hand and Instruments. To the student who isf 

just starting out with his drawing work, the position in which he 
holds his instruments and the free and easy posture of his hands are 
very important. Just as in playing the piano or in any other process 
where manual dexterity is required, this skill can only be attained by 
practice. The following studies should be used in connection with 


I 


Correct 

Position 


£ 


Incorrect Incorrect 

Right Line Pen against T-Square or Triangle 


the instructions given in the forepart of this book and wherever 
references have been given to this section, it is expected that the 
student will study these plates so as to receive helpful suggestions 
in his work. In developing skill in Mechanical Drawing, practice 
is the only method of achieving results after the fundamental princi¬ 
ples have been mastered. A very useful collection of “DON’TS” is 
given herewith and these will bear very close study. 



Position 2. Drawing Pencil Line with T-Square and Triangle 


















MECHANICAL DRAWING 


23 



Position 3. Inking a Line with Pen and T-Square 



Position 4. Drawing Small Circle with the Compass 










24 


MECHANICAL DRAWING 



Position 5 . Drawing Large Circle with Compass with Bent Legs 



Position 6. Drawing Very Large Circle with Spread Compass and Lengthening Bar 













MECHANICAL DRAWING 


25 



Position 7. Adjusting Dividers with One Hand. Note Second and Third Fingers 
between Legs 


“DON’TS” IN DRAFTING WORK 
Don’t fold a drawing. 

Don’t stick the dividers into the drawing board. 

Don’t use the dividers as picks. 

Don’t use the scale to rule lines. 

Don’t fail to clean the table, board, and instruments when beginning 
work. 

Don’t draw on the lower edge of the T-square. 

Don’t cut the sheets of drawing paper with the upper edge of the 
T-square and a knife; use the lower edge. 

Don’t put the end of a pencil in the mouth. 

Don’t oil the compass joints. 

Don’t put away the instruments without cleaning, especially pens. 
Don’t use the cheapest materials. 

Don’t use the T-square as a hammer. 

Don’t screw up the nibs of the pen too tight. 

Don’t use a blotter on lines that have been inked. 

Don’t run the pen or pencil backward over a line. 

Don’t fill a pen over a drawing. 






26 


MECHANICAL DRAWING 


PRELIMINARY LINE PROBLEMS 

To lay out the paper for the plates of this work, place a sheet 
A B G F, Fig. 38, on the drawing board 2 or 3 inches from the left- 
hand edge, called the working edge . If placed near the left-hand 
edge, the T-Square and triangles can be used with greater firmness 
and the horizontal lines drawn with greater accuracy. In fasten¬ 
ing the paper on the board, always true it up with the T-square 
according to the long edge of the sheet and use at least 4 thumb tacks 
—one at each corner. If the paper has a tendency to curl, 6 or 8 



tacks may be used placing them as shown in Fig. 38; many draftsmen 
prefer one-ounce tacks as they offer less obstruction to the T-square 
and triangles. 

To find the center of the sheet place the T-square so that its 
upper edge coincides with the diagonal corners A and G and with the 
corners F and B, and draw short pencil lines intersecting at C. Now 
with the T-square draw through the point C the dot and dash line 
D E, and with the T-square and one of the triangles—shown dotted in 
Fig. 38—draw the dot and dash line II C K. It will probably be 
necessary to draw CK first and then by means of the T-square or 
triangle, produce (extend) CK to II. In this work always move 




























MECHANICAL DRAWING 


27 


the pencil from left to right or from the bottom upward; except in 
certain cases. 

After the center lines are drawn measure off 5 inches above 
and below the point C on the line II C K. These points L and M 
may be indicated by a light pencil mark or by a slight puncture by 
means of one of the points of the dividers. Now place the T-square 
against the left-hand edge of the board and draw horizontal pencil 
lines through L and M. 

Measure off 7 inches to the left and right of C on the center 
line D C E and draw pencil lines through these points N and P, 
perpendicular to DE. These lines form a rectangle 10 inches by 
14 inches, in which all the exercises and figures are to be drawn. 
The lettering of the student’s name and address, date, and plate 
number are to be placed outside of this rectangle in the J-inch margin. 
In all cases lay out the plates in this manner and keep the center lines 
D E and KII as a basis for the various figures. Ink in the border 
line with a heavy line when the drawing is finished. 

Penciling. In laying out the first few plates of this course the 
work is to be done in pencil and then inked in plater the subject of 
tracing the pencil drawings on tracing cloth and the process of making 
blue prints from these tracings will be taken up. Every beginner 
should practice with his instruments until he understands them 
thoroughly and can use them with accuracy and skill. To aid the 
beginner in this work, the first three plates of this course are practice 
plates; they do not involve any problems and none of the work is 
difficult. The student is strongly advised to draw these plates two 
or three times before making the one to be sent to us for correction. 
Diligent practice is necessary at first; especially on Plate I as it in¬ 
volves an exercise in lettering. 

Inking. To ink a drawing well requires great care and some 
experience. The student should not attempt to ink in his work until 
he can make a clear-cut, straight line with ease. It is well to practice 
inking in straight pencil lines, rectangles, and triangles in order to 
improve the work on lines, corners, and intersections. These latter 
should be very definite, each line stopping at exactly the right point. 

Before starting to ink in, adjust the pen by means of the thumb 
screw until a good clear line of the desired width is obtained, making 
frequent test lines, on a piece of material similar to that which is to 


28 


MECHANICAL DRAWING 


be used. Keep the pressure of the pen on the paper uniformly light, 
remembering that different weights of lines are not obtained by pres¬ 
sure as with the ordinary writing pen but only by adjusting the nibs 
of the pen. If the lines are ragged the pen should be put in order, 
according to the instructions already given. Sometimes when the 
ink does not flow regularly, moisten the end of the finger and touch the 
point of the pen. Care should be taken not to put too much ink in 
the pen, but on the other hand there must be enough to draw the 
next line as it is difficult to continue a line after re-filling the pen. 
The only way to draw fine lines well is to frequently clean and re-fill 
the pen. If the amount of ink in the pen is small it is quite likely to 
thicken in the point and cause clogging. When this occurs, draw a 
small strip of paper between the nibs to clean out the clogged ink. 

When drawing, the pen should be held with the thumb screw 
out and should be inclined slightly in the direction in which it is moved. 
Be careful, however, not to incline it too much, as the best of pens 
when incorrectly held will produce poor lines. It is therefore ad¬ 
visable at the start to acquire the correct method of holding the pen. 
Do not press the sides of the pen point too heavily against the ruling 
edge as this will vary the width of the line; after a little practice the 
pen can be lightly and firmly brought in contact with the paper and 
ruling edge at the same time. The pen should be drawn from left 
to right, the hand being steadied by sliding it on the end of the little 
finger. 

Always try to get into the easiest position when inking a line, 
even if it becomes necessary to walk around the drawing. The 
average draftsman prefers the standing position while inking as he 
can usually obtain much better results. Keep the ruling edge be¬ 
tween the line and the body so that the pen will be drawn against the 
ruling edge, for if this is not done, the pen is liable to be pulled off at 
an angle, making a crooked line. Be careful after inking a line to 
draw the ruling edge toward the body away from the line in order 
to avoid blotting. Where lines meet at a point, always ink towards 
the point, being sure to allow one line to dry before inking another. 
Always ink in the top and left-hand lines first, gradually working 
down to the right, thus saving time that otherwise would be lost in 
waiting for the lines to dry. When the pen is set at the proper width, 
draw all the lines of that width before making a change. Never push 


MECHANICAL DRAWING 


29 


the pen backward over a line. If a good line is not drawn the first 
time, it is better to go over it again in the same direction, taking 
great care not to widen the original line. 

Ink dries very quickly and should not be left in the pen on account 
of its corrosive effects. The celluloid triangles should be washed 
frequently in water and all ink spots removed. 

In using the compass, bend both legs so that each will be per¬ 
pendicular to the paper or cloth when the arc or circle is drawn. 
When the pen attachment is used special care must be exercised on 
this point for in no other way can the nibs of the pen be made to bear 
evenly on the surface. In drawing arcs, hold the cylindrical handle 
at the top of the compass loosely between the thumb and the 
forefinger and let it roll between the two during rotation; allow the 
compass to lean slightly in the direction of rotation, pressing down 
the pen point slightly but not the needle point. Be sure to fix the 
needle point firmly in its proper place on the paper before touching 
the pen to the paper, as otherwise a slip is likely to occur. In 
setting the needle down on any particular center, guide it with a 
finger of the left hand. Avoid making a noticeable hole in the paper. 

Ink in the circumference of a circle with one continuous motion, 
giving an even pressure to the pen throughout the operation and stop¬ 
ping it sharply at the end of one revolution. Since straight lines can 
be more easily drawn tangent to curves than the reverse, it is always 
advisable to ink in all arcs or circles first. When a number of circles 
are to be drawn from one center, the smaller should be inked first 
while the center is in the best possible condition. 

PLATE I 

Penciling. To draw Plate 7,* take a sheet of drawing paper at 
least 11 inches by 15 inches and fasten it to the drawing board as 
already explained. Find the center of the sheet and draw fine pencil 
lines to represent the lines DE and HK of Fig. 38. Also draw the 
border lines L, M, N, and P. 

Now measure f inch above and below the horizontal center line 
and, with the T-square, draw lines through these points. These 
lines will form the lower lines DC of Fig. 1 and Fig. 2 and the top 
lines AB of Fig. 3 and Fig. 4. Measure f inch to the right and left 


*Note Instructions, pages 22 to 25, inclusive. 




TH/M THE SHEET TO THE S/ZE SHOWN BY BASH L/NES 






































































MECHANICAL DRAWING 


31 


of the vertical center line; and through these points, draw lines parallel 
to the center line. These lines should be drawn by placing the triangle 
on the T-square as shown in Fig. 38. The lines thus drawn, form the 
sides B C of Fig. 1 and Fig. 3 and the sides AD of Fig. 2 and Fig.4. 
Next draw, with the T-square, the line A B A B 4f inches above the 
horizontal center line, and the line D C D C 4f inches below the hori¬ 
zontal center line. The rectangles of the four figures may now be 
completed by drawing vertical lines 6f inches on each side of the 
vertical center line; these rectangles are each 6J inches long and \\ 
inches wide. 

Fig. 1. Exercise with Line Pen and T-square. Divide the line 
A D into divisions each j inch long, making a fine pencil point or 
slight puncture at each division such as E, F, G, LI, I, etc. Now 
place the T-square with its head at the left-hand edge of the drawing 
board and through these points draw light pencil lines extending to 
the line B C. In drawing these lines the pencil point must pass 
exactly through the division marks so that the lines will be the same 
distance apart. Start each line in the line A D and do not fall short 
of the line B C or run over it. Accuracy and neatness in penciling 
insure an accurate drawing. Some beginners think that they can 
correct inaccuracies while inking; but experience soon teaches them 
that they cannot do so. 

Fig. 2. Exercise with Line Pen, T-square and Triangle. Divide 
the lower line D C of the rectangle into divisions each \ inch long and 
mark the points E, F, G, H, I, J, K, etc., as in Fig. 1. Place the T- 
square about as shown in Fig. 38, and either triangle in position with 
its 90-degree angle at the left. Now draw fine pencil lines from the 
line D C to the line A B passing through the points E, F, G, II, I, J, K, 
etc., keeping the T-square rigid and sliding the triangle toward the right. 

Fig. 3. Exercise with Line Pen T-square and ^5-degree Tri¬ 
angle. Lay off the distances A E, B L, etc., each J inch long on A 
B and B C, respectively. Place the T-square so that the upper edge 
will be below the line D C, and, with the 45-degree triangle, draw the 
diagonal lines through the points laid off. In drawing these lines 
move the pencil away from the body, i. e., from A D to A B and 
from D C to B C. 

Fig. 4. Exercise in Free-Hand Lettering. Draw the center 
line E F, Fig. 39, and light pencil lines Y Z and T X, § inch from the 



32 


MECHANICAL DRAWING 


border lines. With the T-square, draw the line G, J inch from the 
top line and the line H, inch below G. The word “LE T TERING” 
is to be placed between these two lines. Draw the line I, inch below 
II, and space the lines included between I and K, inch apart. 

The next style of letters to be discussed is lower-case letters. 
Draw the line L inch below K and to limit the height of the small 
letters draw a light line J- inch above L. 

Make the space between L and M , inch and draw M and N 
in the same manner as K and L. Now draw 0, ^ inch below N, 



P, A inch below 0, and Q, inch below P. Space Q and R as 
K and L, and draw S, U, V, and W, inch apart. 

The center line is a great aid in centering the word “LETTER¬ 
ING,” the alphabets, numerals, etc. Indent the words “THE” 
and “Proficiency” about | inch, as they are the first words of para¬ 
graphs. To draw the guide lines, mark off distances of J inch on 
any line such as J and with the 60-degree triangle draw light pencil 
lines cutting the parallel lines. Sketch the letters in pencil making 
the width of the ordinary letters such as E, F, II, N, R, etc., about 
f their height. Letters like A, M, and W, are wider. The space 
between the letters depends upon the draftsman’s taste, but the be¬ 
ginner should remember that letters next to an A or an L should be 
placed nearer to them than to letters whose sides are parallel: for 
































MECHANICAL DRAWING 


33 


instance there should be more space between an N and E than be¬ 
tween an E and H. Similarly a greater space should be left on either 
side of an 1 . On account of the space above the lower line of the L y 
a letter following an L should be close to it. If a T follows a T or an 
L follows an L place them near together. In all lettering place the 
letters so that the general effect is pleasing. After the four figures 
are completed, pencil in the lettering for name, address, and date. 
With the T-square draw a pencil line inch above the top border 
line at the right-hand end, and about 3 inches long. At a distance 
of - 5 % inch above this line draw another line of about the same 
length. These are the guide lines for the word Plate I. Pencil the 
letters free-hand using the 60-degree guide lines if desired. 

Draw in a similar manner the guide lines of the date, name, and 
address in the lower margin, the date of completing the drawing placed 
under Eig. 3, and the name and address at the right, under Fig. 4. 
The street address is unnecessary. It is a good plan to draw lines 
/g- inch apart on a separate sheet of paper and pencil the letters in 
order to know just how much space each word will require. The in¬ 
sertion of the words “Fig. 1,” “Fig. 2,” etc., is optional with the 
student, but it is advised that he do this extra lettering for the 
practice as well as for convenience in reference. First draw with the 
T-square two parallel lines inch apart under each exercise, the 
lower line being T V inch above the horizontal center line or above the 
lower border line. 

Inking. After all of the penciling of Plate I has been com¬ 
pleted the exercises should be inked. Before doing this, however, 
see that the pen is in proper condition, and after filling try it on a 
separate piece of paper in order that the proper width of line may be 
drawn. In the first work where no shading is done, use a firm, 
distinct line. The beginner should avoid the extremes; a very light 
line makes the drawing appear weak and indistinct, while a very 
heavy line detracts from its artistic appearance. 

Ink in all the horizontal lines of Fig. 1 first, moving the T-square 
from A to D, and take great care to start and stop the lines exactly 
on the vertical boundary lines. It is necessary to use both triangle 
and T-square for inking A D and B C. In inking Fig. 2 and Fig. 3, 
follow the same directions as for penciling, inking in the vertical and 
oblique lines first and then the border lines. Ink the border lines 






34 


MECHANICAL DRAWING 


of Fig. 4 first and then the border lines of the plate, making the latte 
very heavy and the intersections accurate. The lettering in Fig. - 
should be done free-hand, using a steel pen not finer than a Gillott 404 
Now ink in the four figure numbers, plate number, date, and name 
also free-hand, and then erase the pencil lines. In the finished draw 
ing there should be no center lines, construction lines, or letters othei 
than those in the name, date, etc. 

Cut the sheet 11" X 15", the dash line outside the border line 
of Plate I indicating the edge. 


PLATE II 

Penciling. The horizontal and vertical center lines and the 
border lines for Plate II are laid out in the same manner as were 
those of Plate I. To draw the squares for the six figures, proceed as 
follows: 

Measure off two inches on either side of the vertical center line 
and draw light pencil lines through these points parallel to the vertical 
center line. These lines will form the sides A D and B C of Fig. 2 
and Fig. 5. Parallel to these lines and at a distance of \ inch draw 
similar lines to form the sides B C of Fig. 1 and Fig. 4 and A D of 
Fig. 3 and Fig. 6. The vertical sides AD of Fig. 1 and Fig. 4 and 
R C of Fig. 3 and Fig. 6 are formed by drawing lines perpendicular 
to the horizontal center line at a distance of 6J inches from the center. 

Complete the figures by laying off lines § inch and 4J inches above 
and below the horizontal center line respectively, thus forming six 
4-inch squares. 

In drawing Fig. 1, divide A D and A B into 4 equal parts, then 
draw horizontal lines through E, F, and G and vertical lines through 
L, M, and N. Draw lines from A and B to the intersection 0 of 
lines E and M , and from A and D to the intersection P of lines F and 
L. Similarly draw D J, J C, Cl, and I B. Also connect the points 
J’ &nd I, thus forming a square. The four diamond-shaped 
areas are formed by drawing lines from the middle points of A D, 
A B, B C, and D C to the middle points of lines A P, A O, 0 B, I B, 
etc., as shown in Fig. 1. 

Fig. 2 is an exercise of straight lines. Divide A D and A B 
into four equal parts and draw horizontal and vertical lines as in 
Fig. 1. Now divide these dimensions, A L, M N , etc., and E F } 




MECHANICAL DRAWING 






JANUARY /A, /S/6 HERBERT CHANDLER, CH/CAGO, /LL. 






















































































































































36 


MECHANICAL DRAWING 


G B, etc., into four equal parts—each \ inch—and draw light penci 
lines with the T-square and triangle as shown. 

In Fig. 3, divide A D and A B into eight equal parts, and through ^ 
the points 0, P, Q, 77, 7, J, etc., draw horizontal and vertical lines , 1 
Now draw lines connecting 0 and 77, P and 7, Q and J, etc. As a 
these lines form an angle of 45 degrees with the horizontal, a 45- a 
degree triangle may be used. Similarly from each one of the given c 
points on A B and A D , draw lines at an angle of 45 degrees to B C 
and D C respectively. 

Fig. 4 is drawn with the compasses. Draw the diagonals A C 
and D B, and with the T-square draw the line E 77. Now mark 
off on E 77 distances of \ inch, and with PI as a center describe, by 
means of the compasses, circles having radii respectively 2 inches. 
1} inches, 1 inch, § inch, \ inch, and { inch. Similarly with 77 as a 
center and a radius of 1J inches and lj inches respectively draw the 
arcs F G and 7 J and K L and M N , being careful to end the arcs 
in the diagonals. 

Fig. 5 is an exercise with the line pen and compasses. Draw 
the diagonals A C and D B, the horizontal line L M and the vertical 
line E F passing through the center Q. Mark off distances of J inch 
on L M and E F and complete the squares N R R' N', etc. With 
the bow pencil adjusted so that the distance between the pencil point 
and the needle point is J inch, draw arcs having centers at the corners 
of the inner squares. The arc whose center is N will be tangent to 
the lines A L and A E and the arc whose center is 0 will be tangent 
to N N' and N R. Since the smallest square has 1 inch sides, 
the J-inch arcs drawn with Q as a center will form a circle. 

In Fig. 6, draw the center lines E F and L M, and find the cen¬ 
ters of the four squares thus formed. Through the center 7 draw the 
construction lines HIT and RIP forming angles of 30 degrees 
with EF . Now adjust the compasses to draw circles having a radius 
of one inch, and with 7 as a center, draw the circle 77 P T R. With 
the same radius draw the arcs with centers at A, B, C, and D, and 
also draw the semicircles with centers at 7, F, M, and E. Now draw 
the arcs as shown having centers at the centers of the four squares. 
To locate the centers of the six small circles within the circle IIP T R, 
draw a circle with a radius of inch and having the center in L 
The small circles each have a radius of inch. 




MECHANICAL DRAWING 


37 


Inking. In Plate II ink in only the lines shown full in the speci¬ 
men plate. First ink the star and then the square and diamonds. 
As this is an exercise for practice, the cross-hatching should be done 
without measuring the distance between the lines and without the 
aid of any cross-hatching device. The lines should be about T V inch 
apart. After inking in the plate all construction lines should be 
erased. 

In inking Fig. 2 first ink the principal horizontal and vertical 
lines and then very carefully ink in the short lines. Make these lines 
all of the same width. 

Fig. 3 is drawn entirely with the 45-degree triangle. In inking 
the oblique lines make P I, R K, T M , etc., of the usual width, while 
the alternate lines 0 II, Q J, S L, etc., should be somewhat heavier. 
All of the lines which slope in the opposite direction are light. Now 
ink in the border lines and erase all other horizontal and vertical lines. 

In inking Fig. 4 use only the compasses, adjusting the legs so 
that the pen will always be perpendicular to the paper. In inking 
the arcs, see that the pen stops exactly at the diagonals. The inner 
circle and the next but one should be dotted as shown in the specimen 
plate. After inking the circles and arcs erase the construction lines 
that are without the outer circles, leaving in pencil the diagonals inside 
I the circles. 

In Fig. 5 draw all arcs first and then the straight lines meeting 
these arcs, as it is much easier to make a straight line meet an arc 
or tangent to it, than the reverse. Leave all construction lines in 
pencil. This exercise is difficult, and as in all mechanical and ma¬ 
chine drawing, arcs and tangents are frequently used, the beginner is 
advised to draw this exercise several times. 

Fig. 6 is an exercise with compasses. If the laying out has been 
accurately done in pencil, the inked arcs will be tangent to each other 
and the finished exercise will have a good appearance. If, however, 
the distances were not accurately measured and the lines carefully 
drawn, the inked arcs will not be tangent. The arcs whose centers 
are L, F, M, and E, and A , B, C , and D should be heavier than the 
rest. The small circles may be drawn with the bow pen. After 
inking the arcs all construction lines should be erased. 

Finally ink in the figure numbers, the border lines of the plate, 
name, address, and plate number as in Plate I . 






38 


MECHANICAL DRAWING 


PLATE III 

Penciling. Plate III should be laid out in the same manner 
as Plate II, that is, for size and border lines. In laying out the 
sixteen rectangles, however, the space between the center lines and 
rectangles must in every case be made f inch. Each rectangle is 
to be filled in with what is called section lining , illustrating the 
material of which the object is composed, and, therefore, differing 
accordingly. The conventions here shown are standard, and some 
of them will be used by the student in later work in Machine 
Drawing. Familiarity with them is of value to any draftsman. In 
drawing section lines of this character, the closeness of the lines 
should be governed by the area being sectioned. For large areas I 
use a rather wide spacing; for small areas use a narrow spacing. 1 
In showing a section of any machine, the different parts are dis- 1 
tinguished by altering the slope of the section lines, whether of the 
same material or not. 

Draw the sixteen figures in full and then draw the border lines I 
of the plate. Make the lettering conform to that in Plate I and 
Plate II. 

Inking. After all the penciling of Plate III has been completed, i 
the exercise should be inked, including the titles. 




.CnST IRON I WROUGHT IRON I MftLLERBLE IRON | CRST STEEL 


MECHANICAL DRAWING 


39 



















































































































































































SECTION OF SHOCKLESS JARRING MACHINE 

Courtesy of Tabor Manufacturing Company, Philadelphia, Pennsylvania 













































































































MECHANICAL DRAWING 

PART II 


In Part I the instructions and the problems worked out have 
been designed to teach the student the elementary operations of 
Mechanical Drawing, giving him a knowledge of the instruments, 
an ability to draw a straight and true line, and to make up simple 
figures. A fair degree of drawing ability is now assumed and we 
can pass on to more complicated problems. Wherever we turn 
for subjects, however, we find a knowledge of geometrical figures 
and their properties is absolutely essential to a clear understanding 
of the problems chosen and we will therefore turn to a discussion 
of these geometrical figures and the problems which involve them. 

GEOMETRICAL DEFINITIONS 

A 'point is used for marking position; it has neither length, 
breadth, nor thickness. 

LINES 

A line has length only; it is produced by the motion of a point. 

A straight line or right line is one that has the same direction 
throughout. It is the shortest distance between two points. 

A curved line is one that is constantly changing in direction. 
It is sometimes called a curve. 

A broken line is one made up of several straight lines. 

Parallel lines are lines which lie in the same plane and are equally 
distant from each other at all points. 

A horizontal line is one having the direction of a line drawn 
upon the surface of water that is at rest. It is a line parallel to the 
horizon. 

A vertical line is one that lies in the direction of a thread sus¬ 
pended from its upper end and having a weight at the lower end. 
It is a line that is perpendicular to a horizontal plane. 

An oblique line is one that is neither vertical nor horizontal. 



42 


MECHANICAL DRAWING 


In Mechanical Drawing, lines drawn along the edge of the 
T-square, when the head of the T-square is resting against the left- 
hand edge of the board, are called horizontal lines. Those drawn 
at right angles or perpendicular to the edge of the T-square are 
called vertical lines. 

If two lines cut each other, they are called intersecting lines , 
and the point at which they cross is called the point of intersection. 

ANGLES 

An angle is the measure of the difference in direction of two 
lines. The lines are called sides , and the point of meeting, the 


Fig. 40. Right Angle Fig. 41. Acute Angle Fig. 42. Obtuse Angle 

vertex. Th£ size of an angle is independent of the length of the lines. 

If one straight line meets another (extended if necessary), 
Fig. 40, so that the two angles thus formed are equal, the lines are 
said to be perpendicular to each other and the angles formed are 
called right angles. 

An acute angle is less than a right angle, Fig. 41. 

An obtuse angle is greater than a right angle, Fig. 42. 

SURFACES 

A surface is produced by the motion of a line; it has two dimen¬ 
sions—length and breadth. 

A plane figure is a plane bounded on all sides by lines; the 
space included within these lines (if they are straight lines) is called 
a polygon or a rectilinear figure. 

POLYGONS 

A polygon is a plane figure bounded by straight lines. The 
boundary lines are called the sides and the sum of the sides is called 
the perimeter. 

Polygons are classified according to the number of sides. 

A triangle is a polygon of three sides. 








MECHANICAL DRAWING 


43 


A quadrilateral is a polygon of four sides. 

A pentagon is a polygon of five sides, Fig. 43. 
A hexagon is a polygon of six sides, Fig. 44. 

A heptagon is a polygon of seven sides. 

An octagon is a polygon of eight sides, Fig. 45. 


Fig. 43. Pentagon 



Fig. 44. Hexagon 


Fig. 45. Octagon 


A decagon is a polygon of ten sides. 

A dodecagon is a polygon of twelve sides. 

An equilateral polygon is one all of whose sides are equal. 

An equiangular polygon is one all of whose angles are equal. 

A regular polygon is one all of whose angles and all of whose 
sides are equal. 

Triangles. A triangle is a polygon enclosed by three straight 
lines called sides. The angles of a triangle are the angles formed by 
the sides. 

A right-angled triangle, often called a right triangle, Fig. 46, 
is one that has a right angle. The longest side (the one opposite 



Fig. 46. Right- Fig. 47. Acute Angled 

Angled Triangle Triangle 


Fig. 48. Obtuse-Angled 
Triangle 


the right angle) is called the hypotenuse , and the other sides are 
sometimes called legs. 

An acute-angled triangle is one that has all of its angles acute, 
Fig. 47. 

An obtuse-angled triangle is one that has an obtuse angle, Fig. 48. 
An equilateral triangle is one having all of its sides equal. Fig. 49. 
An equiangular triangle is one having all of its angles equal. 

















44 


MECHANICAL DRAWING 


An isosceles triangle, Fig. 50, is one, two of whose sides are equal. 
A scalene triangle, Fig. 51, is one, no two of whose sides are equal. 



Fig. 49. Equilateral Fig. 50. Isosceles Fig. 51. Scalene Triangle 

Triangle Triangle 


The base of a triangle is the lowest side; it is the side upon which 
the triangle is supposed to stand. Any side may, however, be taken 
as the base. In an isosceles triangle, the side which is not one of 
the equal sides is usually considered as the base. 

The altitude of a triangle is the perpendicular drawn from the 
vertex to the base. 

Quadrilaterals. A quadrilateral is a polygon bounded by four 
straight lines, as Fig. 52. 

The diagonal of a quadrilateral is a straight line joining two 
opposite vertices. 

Trapezium. ( A trapezium is a quadrilateral, no two of whose 
sides are parallel. 

Trapezoid. A trapezoid is a quadrilateral having two sides 



Fig. 52. Quadrilateral Fig. 53. Trapezoid Fig. 54. Parallelogram 


parallel, Fig. 53. Tdie parallel sides are called the bases and the 
perpendicular distance between the bases is called the altitude. 

Parallelogram. A parallelogram is a quadrilateral whose 
opposite sides are parallel, Fig. 54. 

There are four kinds of parallelograms: rectangle, square, 
rhombus, and rhomboid. 

The rectangle, Fig. 55, is a parallelogram whose angles are right 
angles. 

The square, Fig. 56, is a parallelogram all of whose sides 
equal and whose angles are right angles. 


are 










MECHANICAL DRAWING 


45 


The rhombus, Fig. 57, is a parallelogram whose sides are equal 
but whose angles are not right angles. 



Fig. 55. Rectangle 


Fig. 56. Square 



Fig. 57. Rhombus 


The rhomboid is a parallelogram whose adjacent sides are 
unequal, and whose angles are not right angles. 


CIRCLES 

A circle is a plane figure bounded by a curved line called the 
circumference, every point of which is equally distant from a point 
within called the center, Fig. 58. 

A diameter of a circle is a straight line drawn through the center, 
terminating at both ends in the circumference, Fig. 59. 

A radius of a circle is a straight line joining the center with the 



Fig. 58. Circle Fig. 59. Diameter, Fig. 60. Quadrant 

Radius, Tangent 


circumference. All radii of the same circle are equal and their length 
is always one-half that of the diameter. 

An arc is any part of the circumference of a circle. An arc 
equal tq one-half the circumference is called a semi-circumference, 
and an arc equal to one-quarter of the circumference is called a 
quadrant, Fig. 60. A quadrant may mean the arc or angle. 

A chord, Fig. 61, is a straight line which joins the extremities 
of an arc but does not pass through the center of the circle. 

A secant is a straight line which intersects the circumference 
in two points. Fig. 61. 

A segment of a circle, Fig. 62, is the area included between an 
arc and a chord. 








46 


MECHANICAL DRAWING 


A sector is the area included between an arc and two radii drawn 
to the extremities of the arc, Fig. 62. 

A tangent is a straight line which touches the circumference at 
only one point, called the point of tangency or contact, Fig. 59. 



Fig. Cl. Chord and 
Secant 



Fig. 62. Segment Fig. 63. Concentric 

and Sector * Circles 


Concentric circles are circles having the same center, Fig. 63. 
An inscribed angle is an angle whose vertex lies in the circum¬ 
ference and whose sides are chords. It is measured by one-half 
the intercepted arc, Fig. 64. 

A central angle is an angle whose vertex is at the center of the 


circle and whose sides 

are radii, Fig. 65. 


r' x 

/C‘entraC\^ 


I N. Inscr/ted | 

\ N \ Angle 

/N. Angle .X 

c\ 

Fig. 64. Inscribed 

Fig. 65. Central 

Fig. 66. Inscribed 

Angle 

Angle 

Polygon 


An inscribed polygon is one whose vertices lie in the circum¬ 
ference and whose sides are chords. Fig. 66. 


MEASUREMENT OF ANGLES 

To measure an angle, take any convenient radius and describe 
an arc with the center at the vertex of the angle. The portion of 
the arc included between the sides of the angle is the measure of the 
angle. If the arc has a constant radius, the greater the divergence 
of the sides, the longer will be the arc. If there are several arcs 
drawn with the same center, the intercepted arcs will have different 
lengths but they will all be the same fraction of the entire circum¬ 
ference. 





MECHANICAL DRAWING 


47 


In order that the size of an angle or arc may be stated with¬ 
out saying that it is a certain fraction of a circumference, the cir¬ 


cumference is divided into 360 
equal parts called degrees, Fig. 
67. Thus, it may be said that 
a certain angle contains 45 de¬ 
grees, i.e., it is sVt = i of a 
circumference. In order to ob¬ 
tain accurate measurements 
each degree is divided into 60 
equal parts called minutes and 
each minute into 60 equal parts 
called seconds. 



SOLIDS 

A solid has three dimensions—length, breadth, and thickness. 
The most common forms of solids are 'polyhedrons, cylinders, cones , 
and spheres. 

POLYHEDRONS 

A polyhedron is a solid bounded by planes. The bounding planes 
are called faces and their intersections are called edges. The inter¬ 
sections of the edges are called vertices. 

A polyhedron having four faces is called a tetrahedron; one having 
six faces, a hexahedron; one having eight faces, and octahedron, Fig. 68; 
one having twelve faces, a dodecahedron, etc. 

Prisms. A prism is a polyhedron having two opposite faces, 
called bases, which are equal and parallel, and other faces, called 



Fig. 68. Octahedron Fig. 69. Prism Fig. 70. Right Prism 


lateral faces, which are parallelograms, Fig. 69. The altitude of a 
prism is the perpendicular distance between the bases. The area 
of the lateral faces is called the lateral area. 













48 


MECHANICAL DRAWING 


Prisms are called triangular, rectangular, hexagonal, etc., accord¬ 
ing to the shape of the bases. Further classifications are as follows:' 



Fig. 71. Parallelopiped Fig. 72. Rectangular Paral- Fig. 73. Truncated 

lelopiped Prism 


A right prism is one whose lateral faces are perpendicular to 
the bases, Fig. 70. 

A regular prism is a right prism having regular polygons for 
bases. 

Parallelopiped. A parallelopiped is a prism whose bases are 
parallelograms, Fig. 71. If all the edges are perpendicular to the 
bases, it is called a right parallelopiped. 

A rectangular parallelopiped is a right parallelopiped whose 
bases and lateral faces are rectangles, Fig. 72. 

A cube is a rectangular parallelopiped all of whose faces are 
squares. 

A truncated prism is the portion of a prism included between 
the base and a plane not parallel to the base, Fig. 73. 

Pyramids. A pyramid is a polyhedron whose base is a polygon 
and whose lateral faces are triangles having a common vertex called 
the vertex of the pyramid. 



Fig. 74. Pyramid Fig. 75. Regular Pyramid Fig. 76. Frustum of 

Pyramid 


The altitude of the pyramid is the perpendicular distance from 
the vertex to the base. 

Pyramids are named according to the kind of polygon forming 
the base, viz, triangular, quadriangular , Fig. 74. pentagonal , Fig. 75, 
hexagonal . 



















MECHANICAL DRAWING 


49 


A regular 'pyramid is one whose base is a regular polygon and 
whose vertex lies in a perpendicular erected at the center of the base, 

Fig. 75. 

A truncated pyramid is the portion of a pyramid included 
between the base and a plane not parallel to the base. 

A frustum of a pyramid is the solid included between the base 
and a plane parallel to the base, Fig. 76; its altitude is the perpendic¬ 
ular distance between the bases. 


CYLINDERS 

A cylinder is a solid having as bases two equal parallel surfaces 
bounded by curved lines, and as its lateral face the continuous 



Fig. 77. Cylinder Fig. 78. Right Cylinder Fig. 79. Inscribed Cylinder 


surface generated by a straight line connecting the bases and moving 
along their circumferences. The bases are usually circles and such 
a cylinder is called a circular cylinder , Fig. 77. 

A right cylinder , Fig. 78, is one whose side is perpendicular to 
the bases. 

The altitude of a cylinder is the perpendicular distance between 
the bases. 

A prism whose base is a regular polygon may be inscribed in 
or circumscribed about a circular cylinder, Fig. 79. 

CONES 

A cone is a solid bounded by a conical surface and a plane which 
cuts the conical surface. It may be considered as a pyramid with 
an infinite number of sides, Fig. 80. 

The conical surface is called the lateral area and it tapers to a 
point called the vertex; the plane is called the base. 

The altitude of a cone is the perpendicular distance from the 
vertex to the base. 










50 


MECHANICAL DRAWING 


An element of a cone is any straight line from the vertex to the 
circumference of the base. 

A circular cone is a cone whose base is a circle. 

A right circular cone , or cone of revolution, Fig. 81, is a cone 



Fig. 80. Cone 



Cone 



Fig. 82. Frustum of 
Cone 


whose axis is perpendicular to the base. It may be generated by 
the revolution of a right triangle about one of the legs as an axis. 

A frustum of a cone, Fig. 82, is the portion of the cone included 
between the base and a plane parallel to the base; its altitude is the 
perpendicular distance between the bases. 


SPHERES 

A sphere is a solid bounded by a curved surface, every point 
of which is equally distant from a point within called the center. 

The diameter is a straight line drawn through the center and 
having its extremities in the-curved surface. The radius —J diameter 
■—is the straight line from the center to a point on the surface. 

A plane is tangent to a sphere when it touches the sphere in only 


Fig. 83. Plane Tangent to Sphere Fig. 84. Great and Small Circle 

one point. A plane perpendicular to a radius at its outer extremity 
is tangent to the sphere, Fig. 83. 

An inscribed polyhedron is a polyhedron wdiose vertices lie in the 
surface of the sphere. 

A circumscribed polyhedron is a polyhedron whose faces are 
tangent to a sphere. 




MECHANICAL DRAWING 


51 


A great circle is the intersection of the spherical surface and 
a plane passing through the center of the sphere, Fig. 84. 



Fig. 85. Intersections of Plane with Cone and Cylinder Giving Ellipses as Shown in ( b ) and (d) 


A small circle is the intersection of the spherical surface and 
a plane which does not pass through the center, Fig. 84. 

CONIC SECTIONS 

If a plane intersects a cone at various angles with the base the 
geometrical figures thus formed are called conic sections. A plane 
perpendicular to the base passing through the vertex of a right 
circular cone forms an isosceles triangle. If the plane is parallel 
to the base, the intersection of the plane and the conical surfaces 
will be the circumference of a circle. 

Ellipse. If a plane AB, Fig. 85a, 
cuts a cone oblique to the axis of the 
cone, but not cutting the base, the curve 
formed is called an ellipse, as shown in 
Fig. 85b, this view being taken per¬ 
pendicular to the plane AB. If the 
plane cuts a cylinder as shown in big. Fig. 86. Diagram Showing Constanta 

r . TV nri • of Ellipse 

85c, the ellipse shown in Fig. 85d is 

the result, this view being also taken perpendicular to the plane 
AB. An ellipse may be defined as a curve generated by a point 






















52 


MECHANICAL DRAWING 



Fig. 87. Intersection of Plane with Cone, 
Parallel to Element of Cone and Para¬ 
bolic Section Produced 


moving in a plane in such a mam 
ner that the sum of the distances 
from the point to two fixed points 
shall always he constant. 

The two fixed points are 
called foci, Fig. 86, and shall lie 
on the longest line that can be 
drawn in the ellipse which is 
called the major axis; the shortest 
line is called the minor axis; and 
perpendicular to the major axis 
at its middle point, called the center. 

An ellipse may be constructed 
if the major and minor axes are 
given or if the foci and one axis are i 
known. 

Parabola. If a plane AB, Fig. 
87a, cuts a cone parallel to an ele¬ 
ment of the cone, the curve resul ting 
from this intersection is called a 



Fig. 88. Diagram Showing Constants of 
Parabola 



parabola, as shown in Fig. 87b, 
the view being taken perpen¬ 
dicular to the plane AB. This 
curve is not a closed curve for the 
branches approach parallelism. 

A parabola may be defined 
as a curve every point of which 
is equally distant from a line and 



Fig. 90. Diagram Showing Con¬ 
stants of Hyperbola 


a point. 

The point is called the focus, Fig. 88, 
and the given line, the directrix . The 
line perpendicular to the directrix and 
passing through the focus is the axis. 
The intersection of the axis and the curve 
is the vertex. 

Hyperbola. If a plane AB, Fig. 89a, 
cuts a cone parallel to its axis, the 
resulting curve is called a hyperbola, 












MECHANICAL DRAWING 


53 


7 ig. 89b, the view being taken perpendicular to the plane AB. 

Like the parabola, the curve is not closed, the branches con¬ 
stantly diverging. 

A hyperbola is defined as a plane curve such that the difference 
between the distances from any point in the curve to two fixed points 
s equal to a given distance . 

The two fixed points are the foci and the line passing through 
them is the transverse axis, Fig. 90. 

Rectangular Hyperbola. The form of hyperbola most used 
in Mechanical Engineering is called the rectangular hyperbola 
because it is drawn with reference to rectangular coordinates. This 
curve is constructed as fol¬ 
lows: In Fig. 91, OX and 
OY are the two coordinate 
axes drawn at right angles 
to each other. These lines 
are also called asymptotes . 

Assume A to be a known 
point on the curve. Draw 
!AC parallel to OX and 
AD' perpendicular to OX. 

Mark off any convenient 

! points on AC such as E, F, G , and H, and through these points 
draw EE', FF', GG', and HH', perpendicular to OX. Connect 
E, F, G, H, and C with 0 . Through the points of intersection of 
the oblique lines and the vertical line AD' draw the horizontal 
lines LL', MM', NN', FF', and QQ'. The first point on the curve 
is the assumed point A, the second point is F, the intersection of 
1 LI/ and EE', the third the intersection S, and so on. 

In this curve the products of the coordinates of all points are 
equal. Thus LRxRE' = MSxSF'= NTX TG'. 

ODONTOIDAL CURVES 

Cycloidal Curves. Cycloid. The cycloid is a curve generated 
by a point on the circumference of a circle which rolls on a straight 
jine tangent to the circle, as shown at the left, Fig. 92. 

The rolling circle is called the describing or generating circle, 
the point on the circle, the describing or generating point, and the 



Fig. 91. Construction of Rectangular Hyperbola 







54 


MECHANICAL DRAWING 


tangent along which the circle rolls, the director. In order that the 
curve described by the point may be a true cycloid the circle must 
roll without any slipping. 

Hypocycloid. In case the generating circle rolls upon the inside 
of an arc or circle, the curve thus generated is a hypocycloid, 



Fig. 92. Geometrical Constructions for Cycloid and Hypocycloid 


Fig. 92. If the generating circle has a diameter equal to the radius 
of the director circle the hypocycloid becomes a straight line. 

Epicycloid. If the generating circle rolls upon the outside 
of the director circle, the curve generated is an epicycloid, Fig. 93. 

Involute Curves. If a thread of fine wire is wound around a 
cylinder or circle and then unwound, the end will describe an involute 
curve. The involute may be defined as a curve generated by a point 
in a tangent rolling on a circle, known as the base circle, Fig. 94. 



Fig. 93. Geometrical Construction 
for an Epicycloid 



The details of the ellipse, parabola, hyperbola, cycloid, and 
involute will be taken up in connection with the plates. 

The most important application of the cycloidal and involute 
curves is in the cutting of all forms of gear teeth. It has been found 
that the teeth of gears when cut accurately to either of these curves 
will mesh with the least friction and run with exceptional smooth¬ 
ness. The development of these gears and of the machines for 
cutting them has reached a high state of perfection. 









MECHANICAL DRAWING 


55 


GEOMETRICAL PROBLEMS 

The problems given in Plates IV to VIII inclusive have been 
chosen because of their particular bearing on the work of the 
mechanical draftsman. They should be solved with great care, as the 
principles involved will be used in later work. 

PLATE IV 

Penciling. The horizontal and vertical center lines and the 
border lines should be laid out in the same manner as in Plate I. 
Now measure off 2\ inches on both sides of the vertical center line 
and through these points draw vertical lines as shown by the dot 
and dash lines, Plate IV. In locating the figures, place them a little 
above the center so that there will be room for the number of the 
problem. 

Draw in lightly the lines of each figure with pencil and after the 
entire plate is completed, ink them. In penciling, all intersections 
must be formed with great care as the accuracy of the results depends 
upon it. Keep the pencil points in good order at all times and draw 
lines exactly through intersections. 

Problem 1. To bisect a given straight line. 

Draw the horizontal straight line A C about 3 inches long. 
With the extremity A as a center and any convenient radius— 
about 2 inches—describe arcs above and below the line A C. 
With the other extremity C as a center and with the same radius 
draw similar arcs intersecting the first arcs at D and E. The radius 
of these arcs must be greater than one-half the length of the line in 
order that they may intersect. Now draw the straight line D E 
passing through the intersections D and E. This line will cut A C 
at its middle point F. 

Therefore 

AF = FC 

Proof. Since the points D and E are equally distant from A 
and C a straight line drawn through them is perpendicular to AC 
at its middle point F. 

Problem 2. To construct an angle equal to a given angle. 

Draw the line 0 C about 2 inches long and the line Oi of 
about the same length. The angle formed by these lines may be 




RLA TE 


5(3 


MECHANICAL DRAWING 




JANUARY t4, !9/B. HERBERT CHANDLER, CH/CAGO, /LL . 

































































































MECHANICAL DRAWING 


57 


any convenient size—about 45 degrees is suitable. This angle 
A 0 C is the given angle. 

Now draw F G, sl horizontal line about 2 \ inches long, and let 
F, the left-hand extremity, be the vertex of the angle to be con¬ 
structed. 

With 0 as a center and any convenient radius—about 1J inches 
—describe the arc L M cutting both 0 A and 0 C. With F as a 
center and the same radius draw the indefinite arc 0 Q. Now set 
the compass so that the distance between the pencil and the needle 
point is equal to the chord L M. With Q as a center and a radius 
equal to L M draw an arc cutting the arc 0 Q at P. Through 
F and P draw the straight line F E. The angle E F G is the re¬ 
quired angle since it is equal to A 0 C. 

Proof. Since the chords of the arcs L M and P Q are equal, 
the arcs are equal. The angles are equal because with equal radii 
equal arcs are intercepted by equal angles. 

Problems 3 and 4. To draw through a given point a line parallel 
i to a given line . 

First Method. Draw the straight line A C about 3J inches 
long and assume the point P about 1J inches above A C. Through 
the point P draw an oblique line F E forming any convenient angle 
—about 60 degrees—with A C. Now construct an angle equal to 
P F C having its vertex at P and the line E P as one side. (See 
Problem 2.) The straight line P 0 forming the other side of the 
angle E P 0 will be parallel to A C. 

Proof. If two straight lines are cut by a third making the 
corresponding angles equal, the lines are parallel. 

Second Method. Draw the straight line A C about 3J inches 
long and assume the point P about 1| inches above A C. With 
P as a center and any convenient radius—about 2\ inches—draw 
the indefinite arc E D cutting the line A C. Now with the same 
radius and with D as a center, draw an arc P Q. Set the com¬ 
pass so that the distance between the needle point and the pencil 
is equal to the chord P Q. With D as a center and a radius equal 
to P Q, describe an arc cutting the arc E D at H. A line drawn 
through P and H will be parallel to A C. 

Proof. Draw the line Q H. Since the arcs P Q and H D 
are equal and have the same radii, the angles P H Q and H Q D 



58 


MECHANICAL DRAWING 


are equal. Two lines are parallel if the alternate interior angles 
are equal 

Problems 5 and 6. To draw a perpendicular to a line from 
a point in the line. 

First Method. WHEN THE POINT IS NEAR THE MIDDLE OF 
THE LINE. 

Draw the line A C about 3^ inches long and assume the point 
P near the middle of the line. With P as a center and any convenient 
radius—about 1J inches—draw two arcs cutting the line A C at 
E and F. Now with E and F as centers and any convenient radius 
—about 2\ inches—describe arcs intersecting at 0: The line OP 
will be perpendicular to A C at P. 

Proof. The points P and 0 are both equally distant from E 
and F. Hence a line drawn through them is perpendicular to 
E F at P. 

Second Method. WHEN THE POINT IS NEAR THE END OF 
THE LINE. 

Draw the line A C about 3^ inches long. Assume the given 
point P to be about f inch from the end A. With any point D 
as a center and a radius equal to D P, describe an arc cutting A C 
at E. Through E and D draw the diameter E 0. A line from 
0 to P is perpendicular to A C at P. 

Proof. The angle OP E is inscribed in a semicircle; hence 
it is a right angle, and the sides OP and PE are perpendicular 
to each other. 

Lettering. After completing these figures draw pencil lines for 
the lettering. Place the words u Plate IV” and the date and the 
name in the border, as in preceding plates. To letter the words 
‘‘Problem 1,” “Problem 2,” etc., draw three horizontal lines J inch, 
| inch, and t \ inch, respectively, above the horizontal center line 
and the lower border line to serve as a guide for the size of the letters. 

Inking. In inking Plate IV, ink in the figures first. Make the 
line A C, Problem 1, a full line as it is the given line; make the arcs 
and the line D E dotted as they are construction lines. Similarly in 
Problem 2, make the sides of the angles full lines and the chord 
L M and the arcs dotted. Follow the same plan in inking the lines 
of Problems 3, 4, 5, and 6. In Problem 6, ink in only that part of 
the circumference which passes through the points 0, P, and E . 


MECHANICAL DRAWING 


59 


After inking the figures, ink in the heavy border line, and the 
lettering. 

PLATE V 

Penciling. In laying out the border lines and center lines 
follow the directions given for Plate IV. Draw the dot and dash 
lines in the same manner, as there are to be six problems on this plate. 

Problem 7. To draw a perpendicular to a line from a point 
without the line. 

Draw the straight line A C about 3J inches long, and assume 
the point P about 1J inches above the line. With P as a center and 
any convenient radius—about 2 inches—describe an arc cutting A C 
at E and F. The radius of this arc must always be such that it will 
cut A C in two points; the nearer the points E and F are to A and C, 
the greater will be the accuracy of the work. 

Now with E and F as centers and any convenient radius—about 
2J inches—draw the arcs intersecting below A C at T. A line 
through the points P and T will be perpendicular to A C. In case 
there is not room below A C to draw the arcs, they may be drawn 
intersecting above the line as shown at N. Whenever convenient 
draw the arcs below A C for greater accuracy. 

Proof. Since P and T are both equally distant from E and F, 
the line P T is perpendicular to A C. 

Problems 8 and 9. To bisect a given angle. 

First Method. WHEN THE SIDES INTERSECT. 

Draw the lines 0 C and 0 A —about 3 inches long—forming 
any angle of 45 to 60 degrees. With 0 as a center and any con¬ 
venient radius—about 2 inches—draw an arc intersecting the sides 
of the angle at E and F. With E and F as centers and a radius of 
1^ or If inches, describe short arcs intersecting at I. A line 0 D, 
drawn through the points 0 and I, bisects the angle. 

In solving this problem the arc E F should not be too near the 
vertex if accuracy is desired. 

Proof. The central angles AO D and DOC are equal be¬ 
cause the arc E F is bisected by the line 0 D. The point I is equally 
distant from E and F. 

Second Method. WHEN THE LINES DO NOT INTERSECT. 

Draw the lines A C and E F about 4 inches long making an 


3J. V~7c/ 


00 


MECHANICAL DRAWING 




































































































MECHANICAL DRAWING 


61 


angle approximately as shown. Draw A' C' and E' F' parallel to 
A C and E F and at such equal distances from them that they will 
intersect at 0. Now bisect the angle C' O F' by the method given in 
Problem 8. The line 0 R bisects the given angle. 

Proof. Since A' C' is parallel to A C and F' F' is parallel to 
E F, the angle C' 0 F' is equal to the angle formed by the lines 
A C and E F. Hence as 0 R bisects angle C' 0 F' it also bisects 
the angle formed by the lines A C and E F. 

Problem 10. To divide a line into any number of equal parts. 

Let A C —about 3f inches long—be a given line. Suppose 
it is desired to divide it into 7 equal parts. First draw the line A J 
at least 4 inches long, forming any convenient angle with A C. On 
A J lay off, by means of the dividers or scale, points D, E, F, G, etc., 
each \ inch apart. (If dividers are used, the spaces need not be 
exactly \ inch.) Draw the line J C and through the points D, E, 
F, G, etc., draw lines parallel to J C. These parallels will divide 
the line A C into 7 equal parts. 

Proof. If a series of parallel lines, cutting two straight lines, 
intercept equal distances on one of these lines, they also intercept 
equal distances on the other. 

Problem 11. To construct a triangle having given the three sides. 

Draw the three sides, A C, 2f inches long; E F, lyf inches long; 
and M N, 2^ inches long. 

Draw R S equal in length to A C. With R as a center and a 
radius equal to E F describe an arc. With S as a center and a radius 
equal to M N draw an arc cutting the arc previously drawn, at T a 
Connect T with R and S to form the triangle. 

Problem 12. To construct a triangle having given one side and 
the two adjacent angles. 

Draw the line M N 3J inches long and draw two angles A 0 D 
and E F G about 30 degrees and 60 degrees respectively. 

Draw R S equal in length to M N and with R as a vertex and 
R S as one side construct an angle equal to A 0 D. In a similar 
manner construct at*£ an angle equal to E F G. Draw lines from 
R and S through the two established points until they meet at T. 
The triangle RTS will be the required triangle. 

Lettering. Draw the pencil lines and put in the lettering as 
in plates already drawn. 


62 


MECHANICAL DRAWING. 


Inking. In inking Plate V, follow the principles previously ; 
used and do not make certain lines dotted until sure that they should 
be dotted. 

After inking the figures, ink in the border lines and the lettering * 
as already explained. 

PLATE VI 

Penciling. Lay out this plate in the same manner as the pre¬ 
ceding plates. 

Problem 13. To describe an arc or circumference through three 
given 'points not in the same straight line. 

Locate the three points A, B, and C with a distance between 
A and B of about 2 inches and a distance between A and C of about 
2\ inches. Connect A and B and A and C. Erect perpendiculars 
to the middle points of A B and A C as explained in Problem 1. 
Now draw light pencil lines connecting the intersections I and J 
and E and F. These lines will intersect at 0. 

With 0 as a center and a radius equal to the distance O A, 
describe the circumference passing through A, B, and C. 

Proof. The point 0 is equally distant from A, B, and 0, since 
it lies in the perpendiculars to the middle points of A B and A C. 
Hence the circumference will pass through A, B, and C. 

Problem 14. To inscribe a circle in a given triangle. 

Draw the triangle LM N of any convenient size. M N may 
be made 3J inches, L M , 2| inches, and L N, 3| inches. Bisect 
the angles M L N and L M N by the method used in Problem 8. 
The bisectors MI and L J intersect at 0, which is the center of the 
inscribed circle. The radius of the circle is equal to the perpen¬ 
dicular distance from 0 to one of the sides. 

Proof. The point of intersection of the bisectors of the angles 
of a triangle is equally distant from the sides. 

Problem 15. To inscribe a regular pentagon in a given circle. 

With 0 as a center and a radius of about lj inches, describe 
the given circle. With the T-square and triangles draw the center 
lines A C and E F perpendicular to each other and passing through 
0. Bisect one of the radii, 0 C, at H and with this point as a center 
and a radius H E, describe the arc E P. This arc cuts the diameter 
A C at P. With E as a center and a radius E P, draw arcs cutting 


PLA TjE 


MECHANICAL DRAWING 


G3 


































































64 


MECHANICAL DRAWING 


the circumference at L and Q. With the same radius and centers 
at L and Q, draw the arcs cutting the circumference at M and N. 

The pentagon is completed by drawing the chords E L, L M 
MN, NQ, and Q E. 

Problem 16. To inscribe a regular hexagon in a given circle . 

With 0 as a center and a radius of If inches draw the given 
circle. With the T-square draw the diameter A D. With D as 
a center, and a radius equal to 0 D, describe arcs cutting the cir¬ 
cumference at C and E. Now with C and E as centers and the 
same radius, draw the arcs, cutting the circumference at B and 
F. Draw the hexagon by joining the points thus formed. 

Therefore, in order to inscribe a regular hexagon in a circle, 
mark off chords equal in length to the radius. 

To inscribe an equilateral triangle in a circle the same method 
may be used, the triangle being formed by joining the opposite 
vertices of the hexagon. 

Proof. Since the triangle 0 C D is an equilateral triangle by 
construction, the angle C 0 D is one-third of two right, angles and 
one-sixth of four right angles. Hence arc CD is one-sixth of the 
circumference and the chord is a side of a regular hexagon. 

Problem 17. To draw a line tangent to a circle at a given point 
on the circumference. 

With 0 as a center and a radius of about 1J inches draw the 
given circle. Assume some point P on the circumference and join 
the point P with the center 0. By the method given in Problem 6, 
Plate IV, construct a perpendicular to P 0 , which perpendicular 
will be the desired tangent to the circle at the point P. 

Proof. A line perpendicular to a radius at its extremity is 
tangent to the circle. 

Problem 18. To draw a line tangent to a circle from a point 
outside the circle. 

With 0 as a center and a radius of about 1 inch draw the given 
circle. Assume P some point outside of the circle about 2\ inches 
from the center. Draw a straight line passing through P and 0. 
Bisect P 0 and with the middle point F as a center describe the circle 
passing through P and 0. Draw a line from P through the inter¬ 
section of the two circumferences C. The line P C is tangent to the 
given circle. S‘ milarly P E is tangent to the circle. 




MECHANICAL DRAWING 


65 


Proof. The angle P C 0 is inscribed in a semicircle and hence 
is a right angle. Since P C 0 is a right angle, PC is perpendicular 
to CO. The perpendicular to a radius at its extremity is tangent to 
the circumference. 

Inking. In inking Plate VI, the same method should be fol¬ 
lowed as in previous plates. 


PLATE VII 

Penciling. Lay out this plate in the same manner as the pre¬ 
ceding plates. 

Problems 19 and 20. To draw an ellipse when the axes are given. 

First Method. Draw the lines L M and C D about 3J and 2\ 
inches long respectively, making C D perpendicular to L M at its 
middle point P and having C P = P D. The two lines, L M and 
C D f are the axes. With C as a center and a radius L P equal to 
one-half the major axis, draw the arc, cutting the major axis at 
E and F. These two points are the foci. 

Now locate several points on P M, such as A, B, and G. With 
E as a center and a radius equal to L A, draw arcs above and below 
L M. With F as a center and a radius equal to A M describe short 
arcs cutting those already drawn as shown at N. With E as a center 
and a radius equal to L B draw arcs above and below L M as before. 
With F as a center and a radius equal to B M, draw arcs intersecting 
those already drawn as shown at 0. The point R and others are 
found by repeating the process. The student is advised to find at 
least 12 points on the curve—6 above and 6 below L M. These 
12 points with L, C, M, and D will enable him to draw the curve. 

After locating these points, draw a free-hand curve passing 
through them. 

Second Method. Draw the two axes A ** and P Q in the same 
manner as in the first method. With 0 as a center and a radius 
equal to one-half the major axis, describe a circle Similarly with 
the same center and a radius equal to one-half the minor axis, describe 
another circle. Draw any radii such as 0 C, 0 D, 0 E, 0 F, etc., 
cutting both circumferences. These radii may be drawn with the 
60 and 45 degree triangles. From C , D , E , and F, the points of 
intersection of the radii with the large circle, draw vertical lines and 
from C', D'y E' y and F'. the points of intersection of the radii with 


PLA TE 




























MECHANICAL DRAWING 


67 


the small circle, draw horizontal lines The intersections of these 
lines are points on the ellipse. 

Draw a free-hand curve* passing through these points; about 
five points in each quadrant will be sufficient. 

Problem 21. To draw an ellipse by means of a trammel. 

As in Problems 19 and 20, draw the major and minor axes, 
U V and X Y. Take a slip of paper having a straight edge and 
mark off C B equal to one-half the major axis, and D B equal to 
one-half the minor axis. Place the slip of paper in various positions 
keeping the point D on the major axis and the point C on the minor 
axis. If this is done, the point B will mark various points on the 
curve. Find as many points as necessary and sketch the ellipse. 

Problem 22. To draw a spiral of one turn in a circle. 

Draw a circle with the center at 0 and a radius of 1^ inches. 
Locate twelve points, J inch apart on the radius 0 A and draw 
circles through these points. With the 30-degree triangle, draw radii 
OB, OC, OB, etc., 30 degrees apart, thus forming 12 equal parts. 

The points on the spiral are now located; the first is at the 
center 0; the next is at the intersection of the line 0 B and the first 
circle; the third is at the intersection of 0 C and the second circle; 
the other points are located in the same way. Sketch in pencil a 
smooth curve passing through these points. 

Problem 23. To draw a parabola when the abscissa and ordinate 

are given. % 

Draw the straight line A B —about three inches long—as the 
axis, or abscissa of the parabola. At A and B draw the lines EF 
and C B perpendicular to A B, and with the T-square draw E C 
and F B, lj inches above and below A B, respectively. Let A be 
the vertex of the parabola. Divide A E and E C into the same num¬ 
ber of equal parts! Through R, S , T, U } and V, draw horizontal 
lines and connect L , M, N, 0, and P, with A. The intersections 
of the horizontal lines with the oblique lines are points on the curve. 
For instance, the intersection of A L and the line V is one point and 
the intersection of A M and the line U is another. 

The lower part of the curve A B is drawn in a similar manner. 

Problem 24. To draw a hyperbola when the abscissa E X , the 
ordinate A E, and the diameter X Y are given. 


♦See Page 1G, Mechanical Drawing, Part I. 





68 


MECHANICAL DRAWING 


Draw E F about 3 inches long and mark the point X, 1 inch 
from E and the point Y, 1 inch from X. With the triangle and 
T-square, draw the rectangles A B D C and 0 P Q R such that A B 
is 1 inch in length and AC, 3 inches in length. Divide A E and A B 
into the same number of equal parts. Connect Y with the points 
T, U, and V, on A E, and connect X with L , M, and N, on A B. 
The first point on the curve is at A; the next is at the intersection of 
T Y and L X; the third is at the intersection of U Y and M X. 
The remaining points are found in the same manner. Repeat the 
process for X C and the right-hand curve P Y Q. 

Inking. In inking the figures on this plate, use the French or 
irregular curve and make' full lines for the curves and their axes. 
Dot the construction lines as usual. Ink in all the construction 
lines used in finding one-half of a curve, and in Problems 19, 20, 23, 
and 24 leave all construction lines in pencil except those inked. In 
Problems 21 and 22 erase all construction lines not inked. The 
trammel used in Problem 21 may be drawn in the position shown, 
or outside of the ellipse in any convenient place. 

The same lettering should be done on this plate as on previous 
plates 

PLATE VIII 

Penciling. In laying out Plate VIII, draw the border lines 
and horizontal and vertical center lines as in previous plates, divid¬ 
ing the plate into four spaces. 

Problem 25. To construct a cycloid when the diameter of the 
generating circle is given. 

With O' as a center and a radius of £ inch draw a circle, and, 
tangent to it, draw the indefinite horizontal straight line A B. Divide 
the circle into any number of equal parts—12 for instance—and 
through these points of division C, D, E, F, etc.*, draw horizontal 
lines. Now with the dividers set so that the distance between the 
points is equal to the chord of the arc C D, mark off the points L , 
M, N, 0, P, on the line A B, commencing at the point II. At these 
points erect perpendiculars to the center line X O' which is the line 
of centers of the generating circle as it rolls along the line A B. With 
the intersections Q, R, S , T , etc., as centers describe arcs of circles 
as shown. The points on the cycloid will be the intersections of 






FEBRUARY /E, /9/6. HERBERT CHANDLER , CH/CAGO , /LL . 



































































































70 


MECHANICAL DRAWING 


these arcs and the horizontal lines drawn through the points C, D, E, 
F, etc. Thus the intersection of the arc whose center is Q and the 
horizontal line through C is a point J on the curve. Similarly, the 
intersection of the arc whose center is R and the horizontal line 
through D is the point K on the curve. The remaining points on 
the left, as well as those on the right, are found in the same manner. 
To obtain great accuracy in this curve, the circle should be divided 
into a large number of equal parts, because the greater the number 
of divisions the less the error due to the difference in length be¬ 
tween a chord and its arc. 

Problem 26. To construct an epicycloid when the diameter of the ! 
generating circle and the diameter of the director circle are given. 

The epicycloid and the hypocycloid may be drawn in the same j 
manner as the cycloid if arcs of circles are used in place of the hori¬ 
zontal lines. With 0 as a center and a radius of f inch describe 
a circle. Draw the diameter E F of this circle and produce E F 
to G such that the line F G is 2f inches long. With G as a center 
and a radius F G, describe the arc A B of the director circle. With 
the same center G, draw the arc P Q which will be the path of the 
center of the generating circle as it rolls along the arc A B. Now * 
divide the generating circle into any number of equal parts—twelve * 
for instance—and through the points- of division H, /, L, M, and N, I 
draw arcs having G as a center. With the dividers set so that the I 
distance between the points is equal to the chord H I , mark off dis¬ 
tances on the director circle A F B. Through these points of division 
R, S , T, U, etc., draw radii intersecting the arc P Q in the points 
R' } S', T', etc., and with these points as centers describe arcs of circles 
as in Problem 25. The intersections of these arcs with the arcs 
already drawn through the points H, I, L, M, etc., are points on the 
epicycloid. Thus the intersection of the circle whose center is R' 
with the arc drawn through the point H is a point upon the curve. 
Also the arc whose center is S' with the arc drawn through the point 
I is another point on the curve. The remaining points are found 
by repeating this process. 

Problem 27. To draw an hypocycloid when the diameter of the 
generating circle and the radius of the director circle are given. 

With C as a center and a radius of 4 inches describe the arc 
E F, which is the arc of the director circle. Now with the same 




MECHANICAL DRAWING 


71 


center and a radius of Sj inches, describe the arc A B, which is the 
line of centers of the generating circle as it rolls on the director circle. 
With O' as a center and a radius of f inch describe the generating 
circle. As before, divide the generating circle into any number 
i)f equal parts—12, for instance—and with these points of division 
L, M, N, 0, etc., draw arcs having C as a center. Upon the arc 
E F, lay off distances Q R, R S, S T, etc., equal to the chord Q L. 
Draw radii from the points R, S, T, etc., to the center of the director 
circle C and describe arcs of circles having a radius equal to the radius 
of the generating circle, using the points G, /, J, etc., as centers. As 
In Problem 26, the intersections of the arcs are the points on the 
hypocycloid. By repeating this process, the right-hand portion of 
the curve may be drawn. 

Problem 28. To draw the involute of a circle when the diameter 
of the base circle is known. 

With the point 0 as a center and a radius of 1 inch, describe the 
base circle. Divide the circle into any number of equal parts—16, 
for instance—and draw radii to the points of division. At the point 

D, draw a light pencil line perpendicular to 0 D. This line will 
be tangent to the circle. Similarly at the points E, F, G, H, etc., 
draw tangents to the circle. Set the dividers so that the distance 
between the points will be equal to the chord of the arc C D, and 
measure this distance from D along the tangent. From the point 

E, measure on the tangent a distance equal to two of these chords; 
from the point F, three divisions; and from the point G , four divisions. 
Similarly, measure distances on the remaining tangents, each time 
adding the length of the chord. This will give the points L, M, N, 
P, etc., to T. The curve drawn through these points will be the 
involute of the circle. 

Inking. Observe the same rules in inking Plate VIII as were 
given for Plate VII. In Problems 25 and 26 the arcs and lines 
used in locating the points of the other half of the curve may be left 
in pencil. In Problem 28, all construction lines should be inked. 
After completing the problems the same lettering should be done on 
this plate as on previous plates. 


I 






GISHOLT TOOL GRINDER 

Courtesy of Gisholt Machine Company, Madison, Wisconsin 






































































































































MECHANICAL DRAWING 

PART III 


PROJECTIONS 

ORTHOGRAPHIC PROJECTION 

Definitions. Projection. The word projection means to throw 
forward. In mechanical drawing, the significance is to throw forward 
in straight lines. Projection really means, therefore, either the 
act or the result of projecting parallel rays from the surface of a 
body and of cutting these rays with a plane, so as to obtain on the 



plane a shape corresponding point for point with that of the body. 
The rays are called 'projecting lines. A plane may be considered 
transparent, since it is a flat surface having no thickness. 

View. In Fig. 95 a body is shown as projecting from its sur¬ 
face projection lines, and these lines are cut by a plane. By con¬ 
necting the points on the plane made by the projection lines the 


















74 


MECHANICAL DRAWING 


projection of the body is formed, and it corresponds in shape with 
the body itself. A projection of this kind is called a view, this name 
being given it on account of the fact that an observer on the same side 
of the body as the projection plane would get this view. 

It can readily be seen that one view only will not give a com¬ 
plete picture of a solid object. Usually two or more views are 
necessary, according to the complication of the object or body. 
When two or three views are shown, they are pictured on two or 

three planes at right an¬ 
gles to each other. In 
this way views of two 
or three sides are shown, 
and this is usually suffi¬ 
cient to give the idea of 
the complete form of the 
object. 

0 rthographic. The 
word orthographic means 
at right angles, and in 
mechanical drawing, in 
connection with the word 
projection, it means that 
two or more views are 
projected on planes at 
right angles with each other. The various views of a body have 
special names—those showing vertical faces are called elevations, 
such as front, side, end or rear elevation; a view of the top of a 
body is called a plan or plan view; and a view of the under side, a 
bottom view. 

Third-Angle Projection. In Fig. 96 is shown three faces of a 
body projected on three planes—the top view on the top plane, 
the front view on the front plane, and the end view on the end plane. 
It will be seen that the same body is represented as projecting rays 
in three directions, and thus the three projections, or views, are 
obtained. It will also be seen that the three planes with their views 
have been brought into one plane, that is, the surface of the paper. 
This brings the top view directly above the front view, and the end 
view to the right of the front view. The above is a definition of 



Fig. 96. Projections of Top, Front, and End of Body 

























MECHANICAL DRAWING 75 

true projection, usually called third-angle projection, and is the 
method used by practically all draftsmen in this country. 

First-Angle Projection. There is, however, a method called 
first-angle projection, used but little now in this country, although 
formerly in almost general use. Because draftsmen may have to 
do at times with old drawings or drawings made in foreign countries, 
it is well for them to understand first-angle projection. This method 



brings the front view, or elevation, above the top view, or plan, 
the end view being at the right of the front view. Fig. 97 shows 
this method of first-angle projection. 

Comparison of Third- and First-Angle Projection. Perhaps a 
short explanation will make clear the meaning of third- and first- 
angle projection. In geometry, when two planes intersect at right 
angles, the angles are designated as first, second, third, and fourth, 
as numbered in Fig. 97. In first-angle projection, the body is placed 
in angle 1, and a top view is projected on a plane under the body. 














76 


MECHANICAL DRAWING 


This passes the projection lines back through the body, instead 
of throwing them out from the surface. In fact, by this method, 
the body is supposed to turn itself inside out, an absurdity which 
led to the general abandonment of the method in this country. 
Third-angle projection places a body in angle 3, and projects a top 
view on to the plane above it, and a front view on to the plane in 
front of it. This is true projection. 

Projection Methods. When a drawing is made by projection, 
an object is represented just as it would be seen if one eye were 
closed and the other were directly over each point of the object at 
the same time. As an illustration of this, place a box on a table 
and a piece of ground glass a few inches in front of it. Now, stand 



so that one eye will come directly in line with one corner a, Fig. 98. 
Make a dot at cii where the line from the eye to the corner a passes 
through the glass. Next, move the eye until it is directly in line 
with the corner b of the box, and put a dot at b i where the line 
from the eye to the corner b passes through the glass. Repeat 
this process, putting dots on the glass at ci and di where the lines 
from the eye to the corners c and d pass through the glass. Now, 
connect the points ai, b i, c i, and d lf and the complete projection of 
the front of the box will be shown by the figure on the glass. This 

Note. The first four figures in this textbook, Figs. 95, 96, 97, and 98, 
are pictorial views given to show the student clearly how the views of objects 
are projected. The student in drawing orthographic projections does not need 
to draw the pictorial views, but simply the projections, as illustrated in Figs. 99 
to 129, inclusive. 
















MECHANICAL DRAWING 77 

figure is a rectangle, and is the same shape and size as the front 
of the box. 

It is readily seen that from this one projection drawing, or view, 
no idea of the depth of the box is given, although the width and 
height are correctly shown. A top, or plan, view must now be 
made to show the depth of the box. Place another piece of ground 
glass a few inches above the box and, with the eye directly over each 
separate corner of the top, 
repeat the process of making 
the four dots, representing 
each top corner. Connect 
these four dots, and the fig¬ 
ure thus formed represents 
the top projection, or plan 
view, of the box. Now, ar¬ 
range the two pieces of glass, 
as shown in Fig. 99. The 
box being removed, the upper 
glass is simply lowered to the 
table, and the front glass is 
turned from the bottom for¬ 
ward and up, and laid direct¬ 
ly below the upper glass. 

This position of the fig¬ 
ures represents the two pro¬ 
jections—front elevation and 
plan—just as they would be 
drawn by a draftsman on a 
sheet of drawing paper. The 
width of the box is shown in 
both views, and being the 
same in each, the front elevation and plan are both of equal width, 
and therefore each point in the plan is directly over the corre¬ 
sponding point in the front elevation. In more complicated objects, 
where the complete idea cannot be obtained from the front eleva¬ 
tion and plan views, an end view or both end views must be shown 
as in Fig. 100, which represents the projections of a box with a 
curved top. These end views are obtained by taking two or more 



Fig. 99. Plan and Elevation of Box Shown in 
Fig. 98 













78 


MECHANICAL DRAWING 


pieces of ground glass, placing them one in front of each end, and 
then drawing the projections. This is done, as in the cases of the 


i 




Fig. 100. Plan, Elevation, and End Views of a Box with a Curved Top 



Fig. 101. Six Views of Object 

Courtesy of Pennsylvania Railroad Company, Altoona, Pennsylvania 


front elevation and plan, by making several dots for the shape of 
the top, and drawing a curved line through these dots. The two 










































































MECHANICAL DRAWING 


79 


end views are placed as shown—the right-hand view at the right 
of the front view, and the left-hand view at the left. This gives 
the proper arrangement of the views as a draftsman would work 
them out on paper. 

In Fig. 101 is represented a practical case where the object 
is sufficiently complicated to require a view of each of its six faces. 
As will be seen in the figure, six views are shown—front, top, 



Courtesy of Pennsylvania Railroad Company, Altoona, Pennsylvania 

bottom, right side, left side, and rear. In Fig. 102 is represented 
the method of folding out the projection planes after the faces of 
the object have been projected on them, in order to have them all 
in one plane—that of the surface of the drawing paper, as shown 
in Fig. 101. 

Drawing the Projection on Paper. From the explanation just 
given, it will be seen that the projection views are all of the same 
size as the faces of the object they represent. They can, therefore, 






















80 


MECHANICAL DRAWING 


be drawn just as readily on a sheet of drawing paper without the 
use of the ground glass. For the front view, measure the four 
front edges of the object, and lay off on the paper a figure of the same 
shape as the front of the object. Repeat the process for the top 
of the object, obtaining the top view, or plan; and for each end of 
the object, obtaining the end view, or side views. The bottom and 

rear views can be placed in 
the same way. Draw the plan 
view with its four corners di¬ 
rectly over the four corners of 
the front view, and the bot¬ 
tom view with its four cor¬ 
ners directly under. Draw the 
right end, or side, view with 
its four corners directly to the 
right of the four corners of the 
■y front elevation, and the left 
end, or left side, view and rear 
view, with their corners di¬ 
rectly to the left of the cor¬ 
ners of the front view. 

Projection Lines. As each 
projected point of an object 
shown in plan view must be 
directly over the projection of 
the same point in the front 

Fig. 103. Ground Line, xy, at Intersection elevation, a Vertical dotted 
of Horizontal and Vertical Plane9 v_*11 xxi • 

line will connect these points, 
as projected in pairs; and as each projected point in an end 
view must be directly opposite the projection of the same point in 
the front elevation, a horizontal dotted line will connect these 
points, as projected in pairs. These dotted lines are called pro¬ 
jection or construction lines. 

Ground Line. Having the two planes, at right angles, on which 
the front elevation and plan are represented, when the top plane is 
turned up to bring the plan above the front elevation, as repre¬ 
sented on the surface of the drawing paper, it revolves on the inter¬ 
secting line of the two planes as an axis. This intersecting line xy 



Horizontal Plane 
Vertical Plane 









MECHANICAL DRAWING 


81 


in Fig. 103, is called the ground line, and this is usually abbreviated 
to GL. dhe projections may be placed at any convenient distance 
above or below the GL, unless these distances are given in any prob¬ 
lem. In beginning all ordinary projection work, it is customary 
to show the GL as a horizontal line between the front elevation and 
plan views, and the projection of any pair of points in the front 
and plan views are always in a line perpendicular to the GL. This 
is evident from the fact that the points in the plan view are directly 


n B CD 



over the corresponding points in the front elevation. Although 
the ground line is usually used in learning the subject of projections, 
it is customary to omit it in practical work. 

Rules of Projection. (1) If a surface is 'perpendicular to either 
plane of projection, its projection on that plane is simply a line 
a straight line if the surface is plane, a curved line if the surface is 
curved. 

( 2 ) The projected view of any point of any object on a plane 
is in a perpendicular drawn to the plane through the point of the object. 























82 


MECHANICAL DRAWING 


(3) If a straight line is perpendicular to a plane , its projection 
on that plane is a point; and if the straight line is parallel to the plane , 
the projection is a line equal in length to the line itself and makes the 
same angle with the ground line. 

(4) All points on any object at the same height above its base 
must appear in the front elevation at the same distance below the ground 
line, and all points on an object at the same distance back of the front 
face must appear in the plan at the same distance above the ground 
line. 

Typical Examples of Projection. Figs. 104 and 105 show clearly 
several ideas of plan and elevation. In such work as this, it is 



customary to call the vertical plane on which the front elevation 
is drawn V, and the horizontal plane on which the plan is drawn II. 
A= a point A" below H, and B" in front of V 
B = a square prism resting against F, two of its faces parallel 
to II 

C = a circular disk in space para/lel to H 
D= b, triangular card in space parallel to H 
E = a cone with its base resting against F 

F = a cylinder perpendicular to H, and with one end resting 
against H 
















MECHANICAL DRAWING 


83 


G — a line perpendicular to V 

H = a triangular pyramid back of F,with its base resting against H 

PRACTICAL PROBLEMS IN PROJECTION 

1. Square Bar . Fig. 106 represents a square bar. A is the 
front elevation, and shows the length and width of the bar, but not 
the thickness. There must then be another view. B is the plan, 




Fig. 106. Projections of Fig. 107. Projections of Fig. 108. Projections of 

Square Bar Round Bar Hexagonal Bar 

and shows the width and thickness of the bar. From these two 
views the complete form of the bar is obtained and no other views 
are necessary when such is the case. In all working drawings, only 
as many views are shown as is necessary to determine the complete 
form of the object being drawn. 

2. Round Bar . Fig. 107 represents a round bar. The front 
elevation A, shows the width and height of the bar, but does not 
show that it is round. The plan B , shows the circular top of the 
bar and of the proper diameter. In this problem, in addition to the 








































84 


MECHANICAL DRAWING 


dotted projection lines connecting points in plan and elevation, 
it is advisable to put in dot and dash lines for center lines. Pro¬ 
jection lines and center lines are construction lines, 
and may be erased when the drawing is finished, 
unless otherwise ordered. 

3. Hexagonal Bar . Fig. 108 represents a 
hexagonal bar. In this case, center lines should 
be drawn. The front elevation A , shows the 
length of the bar, and the plan B , shows the form 
and the distance between faces. The vertical lines 
in the front elevation show the corners of the 
hexagonal form while both views show the dis¬ 
tance from corner to corner of the hexagonal top. 

4. Hexagonal Nut. Fig. 109 represents a 
hexagonal nut. Center lines should be drawn here also. The front 
elevation A , shows the thickness and width of the nut, and the cir- 



Fig. 109. Projections 
of Hexagonal Nut 



cular hole is shown by heavy dotted lines. Holes are always rep¬ 
resented in this way. The plan B, shows the shape of the top of 
the nut, and also the shape of the hole. 








































MECHANICAL DRAWING 


85 


5. Cylinder with Circular Hole. Fig. 110 represents a cylinder 
with a circular hole passing part way through. Center lines are 
needed here, and in fact where any circle, hexagon, octagon, or other 
shape except a square or rectangle occurs. The front elevation A , 
shows the height and width of the cylinder, 
and the depth and width of hole. The plan 
B, shows the top of the cylinder, its diam¬ 
eter, and the diameter of the hole. 

6. Frustum of Square Pyramid . Fig. 111 
represents a block in the form of a frustum 
of a square pyramid. The front elevation A, 
shows the height of the block, and the width 
of the top and bottom faces. The plan B, 
shows the width and depth of the top and 
bottom faces, and also the edges connecting 
these faces of the frustum. 

7. Square Bar with Cylindrical Portion. 

Fig. 112 represents a square bar with a por¬ 
tion forged to a cylindrical form. The front 
elevation A , shows the length and width of 
the bar, and also the length and width of the 
cylindrical portion. The plan B f shows the 
square top, and by the dotted circle shows 
the shape of the cylindrical portion. The 
fact that this circle is dotted means that the 
cylindrical portion does not come clear 
through to the top. A bottom view C, is 
also shown here, as it gives a better idea of 
the complete form of the bar. Enough views 
should always be showm by the draftsman 
to give the 'workman a clear idea of what 
he is to make. 

8. Circular Ring Made from Round Rod. Fig. 113 represents 
a circular ring made from a round rod. The front elevation A, 
shows the thickness and the diameter of the ring, and the plan B, 
shows the circular form. 

9. Block with Number of Different Dimensions. Fig. 114 rep¬ 
resents a block with a number of different dimensions. The block 



Fig. 112. Projections of 
Square Bar with Cylin¬ 
drical Portion 





























86 


MECHANICAL DRAWING 


has been turned down in such a way that there are five different 
diameters, as shown. All these diameters, and the lengths between, 
may be shown in the front elevation A. From this view, only the 
forms of the cross-section could not be ascertained. Some might 
be square, some hexagonal, or some cir¬ 
cular, but the plan B shows that all are 
circular. 

Summary. The principles of projec¬ 
tion which have been used so far, may 
be stated as follows: 

(1) If a line is parallel to either the verti¬ 
cal or horizontal plane, its actual length is shown 
on that plane, and its other projection is parallel 
to the ground line. 




Fig. 113. Projections of Circular Ring 


Fig. 114. Projections of Turned Block 


(2) A line oblique to either plane has its projections on that plane shorter 
than the line itself, and its other projection oblique to the ground line. 

(3) No projection can be longer than the line itself. 

(4) If two lines intersect, their projections must cross, and the point of 
crossing in the front elevation must be directly under the point of crossing in 
the plan. 

(5) A plane surface, if parallel to either plane, is shown on that plane 
in its true size and shape; if oblique, it is shown smaller than the true size, and 
if perpendicular it is shown as a straight line. 

(6) Lines parallel in space have both their vertical and horizontal pro¬ 
jections parallel. 









































MECHANICAL DRAWING 87 


TRUE LENGTH OF LINES 

Principles. If a line is parallel to a plane, its projection on 
that plane will be equal in length to the line itself, as represented 
in Fig. 115. If a line is perpendicular to a plane, its projection on 



Fig. 115. Projections of a Line Parallel 
to Plane 


X 




-L 


the plane will be a point, as repre¬ 
sented by the cross in Fig. 116. If 
a line is inclined to a plane, its pro¬ 
jection on that plane will be shorter Fig. 116. Projections of a Line Perpen- 

. dicular to Plane 

than the line itself, as represented 

in Fig. 117. If a line is parallel to the horizontal or vertical plane, 
its projection on the other plane will be parallel to the ground line, 
as represented in Fig. 118. A line inclined to both the horizontal 




Fig. 118. Projections of Lines Paral¬ 
lel to Ground Line 


and vertical planes will not show its true length in either projec¬ 
tion, as represented in Fig. 119. In a case like the one last men¬ 
tioned, the true length of the line is found by revolving the line 
until it is parallel to one of the planes. Then, its projection on 
that plane will be its true length. 


















88 


MECHANICAL DRAWING 


True Length by Revolving Horizontal Projection. In Fig. 120 

is shown the horizontal and vertical projections of the line AB, 

and to find the true length 
of the line itself proceed as 
follows: Swing the horizon¬ 
tal projection A h B h about 
one end A h as a pivot, 
until it is parallel to the 
ground line. Project the 
new point Bi downward 
to a point on the vertical 
plane to a line drawn from 
B v parallel to the ground 
line, locating the point Bi. 
The line connecting B\ 
and A v is the true length 
desired, since the true 
length of a line is always 
shown by its projection on 
a plane when the line is parallel to that plane. 

True Length by Revolving Vertical Projection. In Fig. 121 
is shown the method of finding the true length of the same line as 



Fig. 119. True Length of Inclined Line not Shown 
in Its Projections 




in Fig. 120, but by revolving the vertical projection. The method 
is the same. Revolve A V B V about the end B v as a pivot until it is 
parallel to the ground line, and then project Ai v up to Af on the 












MECHANICAL DRAWING 


89 


horizontal plane at the same distance from the ground line as A h . 
The true length is then shown on the horizontal plane by the line 
connecting A\ and B h . Projection lines representing the true 
length are always shown as dot and dash lines, as in Fig. 120 and 121. 

REPRESENTATION OF OBJECTS 

Rectangular Prism or Block. In Fig. 122 there is represented 
a rectangular prism or block, whose length is twice its width. The 
elevation shows its height. 

As the block is placed at an 
angle, three of the vertical 
edges will be visible, and the 
fourth, invisible. In mechan¬ 
ical drawing, the edges, 
which in projection form a 
part of the outline or con¬ 
tour of the figure, must al¬ 
ways be visible, hence are 
always drawn as full lines, 
while the lines or edges which 
are invisible are drawn dot¬ 
ted. The plan shows what 
lines are visible in elevation, 
and the elevation determines 
what are visible in plan. In 
Fig. 122, the plan shows that 
the dotted edge AB is the 
back edge, and in Fig. 123, 
the elevation shows that the 
dotted edge CD is the lower edge of the triangular prism. In gen¬ 
eral, if in elevation an edge projected within the figure is a back 
edge, it must be dotted, and in plan, if an edge projected within 
the outline is a lower edge, it is dotted. 

Triangular Prism or Block. The end view shown in 
Fig. 123 is obtained by projecting the points of the plan across 
to a plane at right angles to the horizontal and vertical planes, 
then revolving them down through 90 degrees and continuing 
the projections to meet the projection lines drawn across from 











90 


MECHANICAL DRAWING 


the elevation. Connecting the points' thus obtained gives the end 
view. End or side views of any object are obtained by projection 

in this way. 

Triangular Block 
with Square Hole. The 
plan, elevation, and end 
views of a triangular 
block with a square hole 
from end to end are 
shown in Fig. 124. In 
this case the plan and 
elevation alone would 
not be sufficient to pos¬ 
itively determine the 
shape of the hole, but 
the end view shows at 
a glance that it is 
square. 



Fig. 123. Projections of a Triangular Prism or Block 



ROTATING AND INCLINING OF OBJECTS 

Method of Rotating Object. The natural way to place an 
object to be shown by projections would be in the simplest position; 
that is, with an edge or face parallel to either the horizontal or 





























MECHANICAL DRAWING 


91 


vertical plane of projection. Sometimes it is necessary, however, 
to draw the views of an object in a position at an angle to the planes. 
In such case it is usually advisable to draw the object parallel to one 
of the planes, and then rotate it to the required position about an 
axis perpendicular to a plane of projection. 

When an object is rotated in this way, about an axis perpen¬ 
dicular to a plane, its projection on that plane will remain unchanged 



Fig. 125. Plan, Front, and Side Views of a Square Pyramid 


in size and shape, and the dimensions parallel to this axis on the 
other planes will remain the same. 

Pyramid. In Fig. 125, the plan, front, and side views of a 
pyramid are shown, and in Fig. 126 is shown the same pyramid 
after it has been rotated through 30 degrees about an axis per¬ 
pendicular to the horizontal plane. The height of the pyramid 
has not been altered by this rotation and, therefore, the front and 
side views are the same height as in the original front view. 

Now, if the pyramid in Fig. 125 is rotated about an axis per¬ 
pendicular to the vertical plane, the front view will not be altered, 














92 


MECHANICAL DRAWING 


and may be copied in the new position at an angle of 30 degrees, 
as shown in Fig. 127. The distances above the ground line to any 
points in the top view are not altered, and the distances of the various 
points can be taken on the lines projected up from the points of the 
front view with a pair of dividers, or the points can be obtained 
by projecting across from the original top view to meet the pro¬ 
jection lines drawn up from the front view. The side view dimen¬ 
sions are not altered, and this view can therefore be obtained in 



planes the points projected across from the top view. 

Cylinder in Inclined Position to Horizontal Plane. As shown 
in Fig. 128, first draw the plan, a circle, at A. Then draw the 
rectangle at B, representing the front view. Now, draw the rec¬ 
tangle at C, representing the front view at the desired angle. This 
rectangle C is the same size as the view at B, since the cylinder 





















Fig. 127. Plan, Front, and Side Views after Revolving Pyramid in Fig. 125 
through 30 Degrees with Horizontal Plane 



Fig. 128. Projections of Cylinder Inclined to Horizontal Plane 






























94 


MECHANICAL DRAWING 


has simply been inclined to the horizontal plane, but kept parallel 
to the vertical plane. The point D, the center of the circle forming 
the base of the cylinder, is projected up to the point E , and with 
this point as a center, a circle representing the plan view of the base 
is drawn. Then from F project up to C, and with this point as 
a center draw the circle representing the plan view of the top of the 



cylinder. Connecting these two circles with horizontal lines HI 
and J K, representing the sides of the cylinder, completes the plan 
view, and the problem is finished. 

As the cylinder is at an angle with the horizontal plane, it 
will be seen that the top and bottom of the cylinder in the plan 
view are not circles, but ellipses. It is, however, customary to draw 
them with the compass, as circles, when the angle of the cylinder 
with the plane is not great. 


































MECHANICAL DRAWING 


95 


Cylinder Greatly Inclined to Horizontal Plane. In Fig. 129 
the plan and front elevation of the top of the cylinder are drawn 
at the desired angle with the horizontal plane at A and B, respec¬ 
tively. The plan view at A is then transferred to C. In each 
of these plan views divide the lower semicircle into a number of 
equal parts, eight in this case. From the view of A, project the 
points 0—8, parallel to the center line, down to E F, and then project 
across to the projection lines drawn vertically down from the points 
0—8 in C. The points of intersection of projection lines, corre¬ 
spondingly numbered, form the shape of the ellipse representing 
the top of the side view of the inclined cylinder D , and the ellipse 
drawn through these points completes this view. The side lines 
of the cylinder may now be drawn, and the curve representing the 
bottom of the side view may easily be copied from the lower half 
of the ellipse representing the top view. When the points have 
been located, the ellipses may be drawn through them with the aid 
of an irregular curve. 

ILLUSTRATIVE EXAMPLES 

1. Construct plan and elevation of a regular hexagonal pyramid . 
It is evident that two distinct geometrical views are necessary to 
convey a complete idea of the form of the object; an elevation to 
represent the sides of the body, and to express its height; and a plan 
of the upper surface to express the form horizontally. 

It is to be observed that this body has an imaginary axis or 
center line, about which the same parts or segments of the body 
are equally distant; this is an essential characteristic of all sym¬ 
metrical figures. 

Draw a horizontal dotted line M N for the center line of the 
plan views, Fig. 130. Then draw a perpendicular ZZ' to M N. 

In delineating the pyramid, it is necessary, in the first place, 
to construct the plan. The point S', where the line ZZ' intersects 
the line M N, is to be taken as the center of the figure, and from 
this point, with a radius equal to the side of the hexagon which 
forms the base of the pyramid, describe a circle, cutting M N in A' 
and D'. From these points, with the same radius, draw four arcs 
of circles, cutting the primary circle in four points. These six points 
being joined by straight lines, will form the figure A B C D E F , 


96 


MECHANICAL DRAWING 


which is the base of the pyramid; and the lines A' D', B r E', and C'F', i 
will represent the projections of its edges foreshortened as they 
would appear in the plan. If this operation has been correctly per¬ 
formed, the opposite sides of the hexagon should be parallel to 
each other and to one of the diagonals; this should be tested By 
the application of the square or other instrument proper for the 
purpose. 

By the help of the plan obtained as above described, the vertical 





projection of the pyramid may be easily constructed. Since it is 
directly under the plan, it must be projected vertically downward; 
therefore, from each of points A', B', C', B', drop perpendiculars 
to AT), the base line of the pyramid in the elevation. The points 
of intersection, A, B, C , and D, are the true positions of all the 
angles of the base; and it only remains to determine the height of 
the pyramid, which is to be set off from the point G to S, and to 

























MECHANICAL DRAWING 


97 


draw SA, SB, S C, and SD, which are the only edges of the pyramid 
visible in the elevation. Of these it is to be remarked that SA 
and SB alone, being parallel to the vertical plane, are seen in their 
true length; and, moreover, that from the assumed position of the 
solid under examination, the points F' and E' being situated in 
the lines BB' and C C', the lines SB and S C are each the projections 
of two edges of the pyramid. 

2. Construct the projections of the pyramid, Example 1, having 
its base set in an inclined position, but with its edges SA and SD 
still parallel to the vertical plane, Fig. 130. 

It is evident, that with the exception of the inclination, the 
vertical projection of this solid is precisely the same as in the pre¬ 
ceding example, and it is only necessary to show the same view of 
the pyramid in its new position. For this purpose, after having 
fixed the position of the point D, draw through this point a straight 
line DA, making with M N an angle equal to the desired inclination 
of the base of the pyramid. Then set off the distance DA, equal 
to that used in Example 1; erect a perpendicular on the center, 
and set off GS equal to the height of the pyramid. Transfer also 
from the first example the distance B G and C G to the corresponding 
points, and complete the figure by drawing the straight lines A S, 
BS, CS, and DS. 

In constructing the plan of the pyramid in this position, it is 
to be remarked that since the edges S A and S D are still parallel 
to the vertical plane, and the point D remains unaltered, the projec¬ 
tion of the points A, D, and S, will still be in the line M N. The 
position of A' is determined by the intersection of the perpendicular 
A A ' with M N. The remaining points, B', C', etc., in the projec¬ 
tion of the base, are found, in a similar manner, by the intersections 
raised from the corresponding points in the elevation, with lines 
drawn parallel to M N, at a distance (set off at o, p) equal to the 
width of the base. By joining all the contiguous points, the figure 
A' B'C' D' E'F' is obtained representing the horizontal projection 
of the base, two of its sides, however, being dotted, as they must 
be supposed to be concealed by the body of the pyramid. The vertex 
S having been similarly projected to S', and joined by straight 
lines to the several angles of the base, the projection of the solid 
is completed. 




98 


MECHANICAL DRAWING 


INTERSECTIONS 

If one surface meets another at some angle, an intersection is 
produced. Either surface may be plane, or curved. If both are 
plane, the intersection is a straight line; if one is curved, the inter¬ 
section is a curve, except in a few special cases; and if both are 
curved, the intersection is usually curved. In the latter case, the 




Fig. 131. Intersection of Plane 
and Square Pyramid 


Fig. 132. Intersection of Plane 
and Triangular Pyramid 


entire curve does not always lie in the same planes. If all points 
of any curve lie in the same plane, it is called a plane curve. A 
plane intersecting a curved surface must always give either a plane 
curve or a straight line. 

Planes with Planes. In Fig. 131 a square pyramid is cut by a 
plane A parallel to the horizontal. This plane cuts from the pyra- 

























MECHANICAL DRAWING 


99 


lid a four-sided figure, the four corners of which will be the points 
here A cuts the four slanting edges of the solid. The plane inter¬ 
sects edge o b at point 4* in elevation. This point must be found 
in plan vertically above on the horizontal projection of line ob, 
that is, at point 4*. Edge oe is directly in front of ob, so is shown 
in elevation as the same line, and plane A intersects oe at point 1* in 




Fig. 134. Intersection of 
Plane and Cone 


elevation, found in plan at \ h . Points 3 and 2 are obtained 
in the same way. The intersection is shown in plan as the square 
1-2-3-4, which is also its true size as it is parallel to the horizontal 
plane. In a similar way the intersections are found in Figs, 132 
and 133. It will be seen that in these three cases where the planes 
are parallel to the bases, the sections are of the same shape as the 
bases, and have their sides parallel to the edges of the bases. 

































100 


MECHANICAL DRAWING 


It is an invariable rule that when such a solid is cut by a plane 
parallel to its base, the section is a figure of the same shape as the 
base. If then in Fig. 134 a right cone is intersected by a plane 
parallel to the base the section must be a circle, the center of which 
in plan coincides with the apex. The radius must equal od. 

In Fig. 135 and Fig. 136 the cutting plane is not parallel to the 
base, hence the section will not be of the same shape as the base. 



Fig. 135. Intersection of Plane 
and Square Pyramid 



Fig. 136. Intersection of Plane 
and Hexagonal Pyramid 


The intersections are found, however, in exactly the same manner 
as in the previous figures, by projecting the points where the plane 
intersects the edges in elevation, on to the other view of the 
same line. 

ILLUSTRATIVE EXAMPLES 

1. Find the horizontal projection of a transverse section of 
the pyramid of Fig. 130, made by a plane perpendicular to the 
vertical, but inclined at an angle to the horizontal plane of projec¬ 
tion; and let all the sides of the base be at an angle with M N, Fig. 137, 






















MECHANICAL DRAWING 


101 


Having drawn the vertical 5 S', the center line of the figures, 
its point of intersection with the line M N is the center of the plan. 
Since none of the sides of the base are to be parallel with M N, draw 
a diameter A'D' making the required angle with M N, and from 
the points A' and D' proceed to set out the angular points of the 
hexagon, as in Fig. 130. Then join the angular points which are 
diametrically opposite and pro¬ 
ject the figure thus obtained 
upon the vertical plane, as shown. 

Now, if the cutting plane 
be represented by the line ad in 
the elevation, it is obvious that 
it will expose, as the section of 
the pyramid, a polygon whose 
angular points being the inter¬ 
sections of the various edges 
with the cutting plane, will be 
projected in perpendiculars drawn 
from the points where it meets 
these edges respectively. From 
the points a, f, b, etc., raise the 
perpendiculars bb', etc., 

to meet the lines A' D', F'C ', 

B' E', etc. When the contiguous 
points of intersection of these 
lines are joined, a six-sided figure 
will be formed which will repre¬ 
sent the section required. The 

„ ^ ~ . . Fig. 137. Frustum of Hexagonal Pyramid 

edges FS and ES being con¬ 
cealed in the elevation, but necessary for the construction of the 
plan, have been expressed in dotted lines, as is also the portion of 
the pyramid situated above the cutting plane which, though sup¬ 
posed to be removed, is necessary in order to draw the lines 
representing the edges. 

2. Find the horizontal projection of the transverse section of a 
regular five-sided pyramid, cut by a plane perpendicular to the 
vertical, but inclined at an angle to the horizontal plane of pro¬ 
jection; and let one edge of the pyramid, BS, be in a plane 




















102 


MECHANICAL DRAWING 




perpendicular to both the horizontal and the vertical planes of 
projection, as shown in Fig. 138. 

The plan of the pyramid is constructed by describing from the 
center S' a circle circumscribing the base, and from B' dividing 
the circumference into five equal parts, and joining the contiguous 
points of division by straight lines. These form the polygon 

A' B'C' D' E', whose angles, when 
joined to the center S', show the 
projections of the edges of the pyra¬ 
mid. Then, following the method 
above explained, the elevation and 
the horizontal projection of the 
section made by the plane a c are 
obtained. But that method will 
not suffice for the determination 
of the point b', because the per¬ 
pendicular let fall from the cor¬ 
responding point b, in the eleva¬ 
tion, coincides with the projection 
of the edge B S. Let the pyramid 
supposedly be turned a quarter 
of a revolution round its axis; 
the line B'S' will then have 
assumed the position S' 6 2 . Pro¬ 
ject the point b 2 to b 3 , and join 
S b z . Then since the required point 
must also be conceived to have 
described a quarter of a circle in 
a plane parallel to the horizontal 
plane, and that its new position 
must be in the line S b 3 , it is obvious that its vertical projection is 
the point b A , the intersection of a horizontal line drawn through b 
with the line S 6 3 . The distance b 6 4 may then be used to determine 
the distance from S' to b', and determines the position of the latter 
point in the plan; or, following a more methodical process, by pro¬ 
jecting the point ¥ to b 5 , and describing a circle from the center 
S' passing through b 5 , its intersection with B'S' is the point 
sought. 



Fig. 138. Frustum of Pentagonal Pyramid 


















MECHANICAL DRAWING 


103 


Planes with Cones or Cylinders. Sections cut by a plane 
from a cone have already been defined as conic sections. These 
sections may be any of the following: two straight lines, circle, 
ellipse, parabola, hyperbola. All except the parabola and hyper¬ 
bola may also be cut from a cylinder. 

Methods have previously been given for constructing the 
ellipse, parabola, and hyper¬ 
bola, without projections; 
it will now be shown that 
they may be obtained as 
actual intersections/ 

Ellipse. In Fig. 139 
the plane cuts the cone 
obliquely. To find points 
on the curve in plan take 
a series of horizontal planes 
xyz, etc., between points 
c° and d°. One of these 
planes, as w, should be taken 
through the center of cd. 

The points c and d must be 
points on the curve, since 
the plane cuts the two con¬ 
tour elements at these 
points. Contour elements 
are those forming the out¬ 
line. The horizontal pro¬ 
jections of the contour ele¬ 
ments will be found in a Elapse— Section from a Cone 

horizontal line passing 

through the center of the base; hence the horizontal projection of 
c and d will be found on this center line, and will be the extreme 
ends of the curve. 

The plane x cuts the siirf ace of the cone in a circle, as it is parallel 
to the base, and the diameter of the circle is the distance between 
the points where x crosses the two contour elements. This circle, 
lettered x on the plan, has its center at the horizontal projection of 
the apex. The circle z and the curve cut by the plane are both on 























104 


MECHANICAL DRAWING 


the surface of the cone, and their vertical projections intersect at 
the points 2-2. Point 2 on the elevation then represents two points 
which are shown in plan directly above on the circle x , and are 
points on the required intersection. Planes y and z, and as manj 
more as may be necessary to determine the curve accurately, are 
used in the same way. The curve found is an ellipse. The student 
will readily see that the true size of this ellipse is not shown in 

the plan, for the plane containing 
the curve is not parallel to the 
horizontal. 

In order to find the actual size 
of the ellipse, it is necessary to place 
its plane in a position parallel either 
to the vertical or to the horizontal. 
The actual length of the long diam¬ 
eter of the ellipse must be shown in 
elevation, c v d v , because the line is 
parallel to the vertical plane. The 
plane of the ellipse then may be 
revolved about c v d° as an axis until 
it becomes parallel to V, when its 
true size will be shown. For the sake 
of clearness of construction, c v d v is 
imagined moved over to the posi¬ 
tion c'd', parallel to c v d\ The lines 
1-1, 2-2, 3-3 on the plan show the 
true width of the ellipse, as these 
lines are parallel to //, but are pro¬ 
jected closer together than their 
actual distances. In elevation these 
lines are shown as the points 1, 2, 3, 
at their true distance apart. Hence if the ellipse is revolved 
around its axis c v d v , the distances 1-1, 2-2, 3-3 may be laid off on 
lines perpendicular to c v d v , and the true size of the figure be shown. 

In Fig. 140 a plane cuts a cylinder obliquely. This is a simpler 
case, as the horizontal projection of the curve coincides with the 
base of the cylinder. To obtain the true size of the section, which 
is an ellipse, any number of points are assumed on the plan and 



Fig. 140. Ellipse—Section from 
Cylinder 















MECHANICAL DRAWING 


105 


projected down on the cutting plane, at 1, 2, 3, etc. The lines drawn 
through these points perpendicular to l'-7' are made equal in length 
to the corresponding distances 2'-2', 3'-3', etc., on the plan, because 
2'-2' is the true width of curve at 2. 

Parabola. If a cone is intersected by a plane which is parallel 
to only one of the elements, as in Fig. 141, the resulting curve is 


Fig. 141. Parabola—Section from a Cone 



the parabola , the construction of which is exactly similar to that for 
the ellipse, as given in Fig. 139. If the intersecting plane is parallel 
to more than one element, or is parallel to the axis of the cone, a 
hyperbola is produced. 

In Fig. 142, the vertical plane A is parallel to the axis of the 
cone. In this instance the curve when found will appear in its true 












106 


MECHANICAL DRAWING 


size, as plane A is parallel to the vertical. Observe that the highest 
point of the curve is found by drawing the circle X on the plan 

tangent to the given plane. 
One of the points where 
this circle crosses the diam¬ 
eter is projected down to 
the contour element of the 
cone, and ’ the horizontal 
plane X drawn. Interme¬ 
diate planes Y, Z, etc., are 
chosen, and corresponding 
circles drawn in plan. The 
points where these circles 
are crossed by the plane A 
are points on the curve, 
and these points are pro¬ 
jected down to the eleva¬ 
tion on the planes Y, Z, etc. 

DEVELOPMENT OF 
SURFACES 

General Details of 
Process. A surface may 
be considered as formed by 
the motion of a line. Any 
length of line moved side- 
wise in any direction will 
form a surface, of a width 
equal to the length of the 
line, and of a length equal 
to the distance over which 
the line is moved. There 
are two different classes 
of surfaces; namely, those 
formed by a moving 

straight line, and those formed by a moving curved line. 

In some construction work, patterns of different faces or of 
the whole surface must be made; in stone cutting, for example, 



Fig. 142. Hyperbola—Section from a Cone 





























MECHANICAL DRAWING 


107 


there must be a pattern giving the shape of any irregular surface, 
and in sheet-metal work a pattern must be made such that, when a 
sheet is cut, it can be so formed that it will be of the same shape 
as the original object. 

This pattern making, or the laying out of a complete surface 
on one plane, is called the development of the surface. Any surface 



which can be smoothly wrapped about by a sheet of paper, can be 
developed. Figures made up of planes and single curved surfaces 
only would be of this nature. Double curved surfaces and warped 
surfaces cannot be developed, and patterns of such surfaces, when 
desired, must be made by an approximate method which requires 
two or more pieces to make the complete pattern. 



By finding the true size of all the faces of an object made up 
of planes, and joining them in order at their common edges, the 
developed surface will be formed. The best way to do this is to 
find the true length of the edges of the object. 

Right Cylinder. In Fig. 143 is represented a right cylinder 
rolling on a plane. The development is formed by one complete 












108 


MECHANICAL DRAWING 


revolution of the cylinder and is a rectangle, the width being equal 
to the height of the. cylinder and the length to the circumference. 

Right Cone. In Fig. 144 is represented a right cone rolling 
out its development, which is a sector of a circle. The arc equals 
the circumference of the circle forming the base of the cone, and 
the radius equals the slant height. 

The projections of any object must be drawn before the develop¬ 
ment can be made, but it is necessary only to draw such views as 
are required for finding the lengths of elements, and true sizes of 
cut surfaces. 

Rectangular Prism. In order to find the development of the 
rectangular prism in Fig. 145, the back face, 1-2-7-6, is supposed 



& 


Fig. 145. Development of Hollow Rectangular Prism 


to be placed in contact with some plane, then the prism turned 
on the edge 2-7 until the side 2-3-8-7 is in contact with the same 
plane, and this process continued until all four faces have been placed 
on the same plane. The rectangles 1-2-3-4 and 6-7-8-5 are for the 
top and bottom, respectively. The development then is the exact 
size and shape of a covering for the prism. If a rectangular hole 
is cut through the prism, the openings in the front and back faces 
will be shown in the development in the centers of the two broad 
faces. 





















MECHANICAL DRAWING 


109 


The development of a right prism, then, consists of as many 
rectangles joined together as the prism has sides, these rectangles 
being the exact size of the faces of the prism, and in addition two 
polygons the exact size of the bases. It will be found helpful in 
developing a solid to number or letter all of the corners on the 
projections, then designate each face when developed in the same 
way as in the figure. 

Cone. If a cone be placed on its side on a plane surface, one 
element will rest on the surface. If now the cone be rolled on the 



7 

Fig. 147. Development of Cone 


Fig. 146. Plan and Elevation 
of Cone 


plane, the vertex remaining stationary until the same element is 
in contact again, the space rolled over will represent the develop¬ 
ment of the convex surface of the cone. Fig. 146 is a cone cut by 
a plane parallel to the base. In Fig. 147, let the vertex of the cone 
be placed at F, and one element of the cone coincide with VF 1. 
The length of this element is taken from the elevation, Fig. 146, 
of either contour element. All of the elements of the cone are of 
the same length, so that when the cone is rolled, each point of the 
base as it touches the plane will be at the same distance from the 
vertex. From this it follows that in the development of the base, 








110 


MECHANICAL DRAWING 


the circumference will become the arc of a circle of radius equal 
to the length of an element, and of a length equal to the distance 
around the base. To find this length divide the circumference 
of the base in the plan into any number of equal parts, say twelve, 
and lay off twelve such spaces, 1 .... 13 along an arc drawn with 
radius equal to VI; join 1 and 13 with V, and the resulting sector 
is the development of the cone from vertex to base. In order to 
represent on the development the circle cut by the section plane DF, 
draw, from the vertex V as a center and with VF as a radius, the 
arc F C. The development of the frus¬ 
tum of the cone will be a portion of a 
circular ring. This of course does not 
include the development of the bases, 
which would be simply two circles the 
same sizes as shown in plan. 



Fig. 148. Plan and Elevation 
of Triangular Pyramid 



Fig. 149. Development of Triangular Pyramid 


Regular Triangular Pyramid. Fig. 148 represents the plan and 
elevation of a regular triangular pyramid, and Fig. 149 its develop¬ 
ment. If face C is placed on the plane its true size will be shown 
in the development. The true length of the base of triangle C is 
shown in the plan. As the slanting edges, however, are not parallel 
to the vertical, their true length is not shown in elevation but must 
be obtained by the method given on page 88, as indicated in Fig. 148. 
The triangle may now be drawn in its full size at C in the develop¬ 
ment, and as the pyramid is regular, two other equal triangles, 










MECHANICAL DRAWING 


111 


D and E, may be drawn to represent the other sides. These, together 
with the base F, constitute the complete development. 

Truncated Circular Cylinder. If a truncated circular cylinder 
is to be developed, or rolled upon a plane, the elements, being 
parallel, will appear as parallel lines, and the base line being per¬ 
pendicular to the elements, will appear as a straight line of length 
equal to the circumference of the base. The base of the cylinder 
in Fig. 150 is divided into twelve equal parts, 1, 2, 3, etc., and com¬ 
mencing at point 1 on the development, these twelve equal spaces 
are laid off along the straight line, giving the total width. 



Draw in elevation the elements corresponding to thte various 
divisions of the base, and note the points where they intersect the 
oblique plane. As the cylinder is rolled beginning at point 1, the 
successive elements, 1, 12, 11, etc., will appear at equal distances 
apart, and equal in length to the lengths of the same elements in 
elevation. Thus point number 10 on the development is found by 
projecting horizontally across from 10 in elevation. It will be seen 
that the curve formed is symmetrical, the half on the left of 7 being 
similar to that on the right. The development of any similar surface 
may be found in the same manner. 

The principle of cylinder development is used in laying out 
elbow joints, pipe ends cut off obliquely, etc. In Fig. 151 is shown 
















112 


MECHANICAL DRAWING 


plan and elevation of a three-piece elbow and collar, and develop¬ 
ments of the four pieces. In order to construct the various parts 
making up the joint, it is necessary to know what shape and size 
must be marked out on the flat sheet metal so that when cut out 
and rolled up the three pieces will form cylinders with the ends 
fitting together as required. Knowing the kind of elbow desired, 
first draw the plan and elevation, and from these make the develop- 



Fig. 151. Plan, Elevation, and Development of Three-Piece Elbow and Collar 


ments. Let the lengths of the three pieces A, B, and C be the same 
on the upper outside contour of the elbow, the piece B at an angle 
of 45 degrees; the joint between A and B bisects the angle between 
the two lengths, and in the same way the joint between B and C. 
The lengths A and C will then be the same and one pattern will 
answer for both. The development of A is made exactly as just 
explained for Fig. 150, and this is also the development of C. 

It should be borne in mind that in developing a cylinder the 
base must always be at right angles to the elements, and if the 
cylinder as given does not have such a base, it becomes necessary 



















































MECHANICAL DRAWING 


113 


to cut the cylinder by a plane perpendicular to the elements, and 
use the intersection as a base. This point must be clearly under¬ 
stood in order to proceed intelligently. A section at right angles 
to the elements is the only section which will unroll in a straight 
line, and is, therefore, the section from which the other sections 
must be developed. As B, Fig. 151, has neither end at right angles 
to its length, the plane X is drawn at the middle and perpendicular 
to the length. B has the same diameter as C and A, so the section 
cut by X will be a circle of the same diameter as the base of A, 
and is shown in the development at X. 

The elements on B are drawn from the points where the elements 
on the elevation of A meet the joint between A and B, and are equally 
spaced as shown on the plan of A. Commencing with the left- 
hand element in B, the length of the upper element between X 
and the top corner of the elbow is laid off above X, giving the first 
point in the development of the end of B fitting with C. The lengths 
of the other elements in the elevation of B are measured in the 
same way and laid off from X . The development of the other 
end of the piece B is laid off below X , using the same distances, 
since X is half way between the ends. The development of the 
collar is simply the development of the frustum of a cone, which 
has already been explained, Fig. 147. The joint between B and 
C is shown in plan as an ellipse, the construction of which the student 
should be able to understand from a study of the figure. 

ISOMETRIC PROJECTION 

Isometric of a Cube. In orthographic projection an object 
has been represented by two or more projections; another system, 
called isometrical drawing, is often used to show in one view the three 
dimensions of an object, length (or height), breadth, and thickness. 
An isometrical drawing of an object, as a cube, is called for brevity 
the isometric of the cube. 

To obtain a view which shows the three dimensions in such a 
way that measurements may be taken from them, draw the cube in 
the simple position shown at the left, Fig. 152, with two faces parallel 
to V; the diagonal from the front upper right-hand corner to the back 
lower left-hand corner is indicated by the dotted line. Swing the 
cube around until the diagonal is parallel with V, as shown in the 



114 


MECHANICAL DRAWING 


second position. Here the front face is at the right. In the third 
position the lower end of the diagonal has been raised so that it is 
parallel to II, becoming thus parallel to both planes. The plan 
is found by the principles of projection, from the elevation and the 
preceding plan. The front face is now the lower of the two faces 
shown in the elevation. From this position the cube is swung around, 
using the corner as a pivot, until the diagonal is perpendicular to 
V but still parallel to II. The plan remains the same, except as 
regards position; while the elevation, obtained by projecting across 
from the previous elevation, gives the isometrical projection of the 
cube. The front face is now at the left. 

Distinction between Isometric Projection and Isometric Drawing . 
In the last position, as one diagonal is perpendicular to V , it follows 



that all the faces of the cube make equal angles with V, hence 
are projected on that plane as equal parallelograms. For the same 
reason all the edges of the cube are projected in elevation in equal 
lengths, but, being inclined to V, appear shorter than they actually 
are on the object. Since they are all equally foreshortened and since 
a drawing may be made at any scale, it is customary to make all the 
isometrical lines of a drawing full length. This will give the same 
proportions, and is much the simpler method. Herein lies the dis¬ 
tinction between an isometric projection and an isometric drawing. 

It will be noticed that the figure may be inscribed in a circle, 
and that the outline is a perfect hexagon. Hence the lines showing 

























MECHANICAL DRAWING 


115 


breadth and length are 30-degree lines, while those showing height 
are vertical. 

True Length of Lines. Fig. 153 shows the isometric of a cube 
1 inch square. All of the edges are shown in their true length, hence 



Fig. 153. Isometric of a Cube Fig. 154. Plan and Ele¬ 

vation of a Cube 


all the surfaces appear of the same size. 
In the figure the edges of the base are 
inclined at 30 degrees with a T-square 
line, but this is not always the case. For 
rectangular objects, such as prisms, cubes, 
etc., the base edges are at 30 degrees 
only when the prism or cube is sup¬ 
posed to be in the simplest possible 
position. The cube in Fig. 153 is sup¬ 
posed to be in the position indicated by 
plan and elevation in Fig. 154, that is, 
standing on its base, with two faces 
parallel to the vertical plane. 

If the isometric of the cube in the 
position shown in Fig. 155 were required, 
it could not be drawn with the base 
edges at 30 degrees; neither would these 
edges appear in their true lengths. It 



















116 


MECHANICAL DRAWING 


follows, then, that in isometrical drawing, true lengths appear 
only as 30-degree lines or as vertical lines. Edges or lines that in 



only by reference to their projectio 
explained in the section on "Oblique 


actual projection are either 
parallel to a T-square line or 
perpendicular to V, are drawn : 
in isometric as 30-degree lines, 
full length; and those that are 
actually vertical are made 
vertical in isometric, also full 
length. 

Three Isometric Axes. In ; 
Fig. 152, lines such as the 
front vertical edges of the ; 
cube and the two base edges 
are called the three isometric 
axes. The isometric of objects 
in oblique positions, as in 
Fig. 155, can be constructed 
ns, by methods which will be 
Projection”, page 123. 



Applications of Isometric Pro¬ 
jections. In isometric drawing 
small rectangular objects are more 
satisfactorily represented than 
large curved ones. In woodwork, 
mortises and joints and various 
parts of framing are well shown 
in isometric. This system is used 
also to give a kind of bird’s-eye 
view of mills or factories. It is also 
used in making sketches of small 
rectangular pieces of machinery, 
where it is desirable to give shape 
and dimensions in one view. 

Characteristics of Various 
Isometrics. Cube with Inscribed 


Circles. Fig. 156 shows a cube with circles inscribed in the t< 
and two side faces. The isometric of a circle is an ellipse, tl 













MECHANICAL DRAWING 


117 


exact construction of which would necessitate finding a number 
of points; for this reason an approximate construction by arcs of 
circles is often made. In the method, Fig. 156, four centers are 
used. Considering the upper face of the cube, lines are drawn 
from the obtuse angles / and e to the centers of the opposite sides. 
The intersections of these lines give points g and h, which serve 
as centers for the ends of the ellipse. With g as center and radius 
ga, the arc ad is drawn, and with / as center and radius fd, the arc 




Fig. 159. Isometric of a Wooden 
Brace 


dc is drawn; the ellipse is finished by using centers h and e. This 
construction is applied to all three faces. 

Cylinder. Fig. 157 is the isometric of a cylinder standing 
on its base. 

Blocks. Fig. 158 represents a block with smaller blocks pro¬ 
jecting from three faces. 

Framework. Fig. 159 shows a framework of three pieces, 
two at right angles and a slanting brace. The horizontal piece is 
mortised into the upright as indicated by the dotted lines. 

House. In Fig. 160 the isometric outline of a house is repre¬ 
sented, showing a dormer window and a partial hip roof; ab is a hip 
rafter, c d a valley. Let the pitch of the main roof be shown at B, 
and let m be the middle point of the top of the end wall of the house. 
Then, by measuring vertically up a distance m l equal to the vertical 










118 


MECHANICAL DRAWING 


height an shown at B, a point on the line of the ridge will be found 
at l. Line li is equal to b h , and i h is then drawn. Let the pitch 
of the end roof be given at A. This shows that the peak of the roof, 
or the end a of the ridge, will be back from the end wall a distance 
equal to the base of the triangle at A. Hence, lay off from l this 
distance, giving point a, and join a with b and x. 

The height k e of the ridge of the dormer roof is known, and it 
must be found where this ridge will meet the main roof. The ridge 
must be a 30-degree line as it runs parallel to the end wall of the house 
and to the ground. Draw from e a line parallel to b h to meet a 
vertical through h and /. This point is in the vertical plane of 



the end wall of the house, hence in the plane of ih. If now a 30- 
degree line be drawn from / parallel to xb , it will meet the roof of 
the house at g. The dormer ridge and fg are in the same horizontal 
plane, hence will meet the roof at the same distance below the ridge 
ai. Therefore draw the 30-degree line g c, and connect c with d. 

Box with Cover . In Fig. 161 a box is shown with the cover 
opened through 150 degrees. The right-hand edge of the bottom 
shows the width, the left-hand edge shows the length and the vertical 
edge shows the height. The short edges of the cover are not 
isometric lines, hence are not shown in their true lengths; neither 
is the angle through which the cover is opened represented in its 
actual size. 











MECHANICAL DRAWING 119 

The corners of the cover must then be determined by co-ordinates 
from an end view of the box and cover. As the end of the cover 



is in the same plane as the end of the box, the simple end view as 
shown in Fig. 162 will be sufficient. Extend the top of the box to 
the right, and from c and d 
let fall perpendiculars on 
ab produced, giving the 
points e and /. The point 
c may be located by means 
of the two distances or co¬ 
ordinates be and ec , and 
these distances will appear 
in their true lengths in the 
isometric view. Hence pro¬ 
duce a'b' to e ' and /'; and 
from these points draw ver¬ 
ticals e'c' and fd'; make Ve f equal to be, e'c' equal to ec; and simi¬ 
larly for d'. Draw the lower edge parallel to c'd' and equal to it 
in length, and connect with b '. 














120 


MECHANICAL DRAWING 


It will be seen that in isometric drawing parallel lines always 
appear parallel. It is also true that lines divided proportionally 
maintain this same relation in isometrxC drawing. 

Prism with Semicircular 



Fig. 164. Plan and Elevation of 

Fig. 165. Isometric of Fig. 164 Oblique Pentagonal Pyramid 


the back face are found by projecting the front centers back 30 
degrees equal to the thickness of the prism, as shown at a and h. 

Pyramid. The plan and elevation of an oblique pentagonal 
pyramid are shown in Fig. 164. It is evident that none of the edges 























MECHANICAL DRAWING 


121 


of the pyramid can be drawn in isometric as either vertical or 30- 
degree lines; hence a system of co-ordinates must be used as shown 
in Fig. 165. This problem illus¬ 
trates the most general case; 
and to locate some of the 
points three co-ordinates must 
be used, two at 30 degrees 
and one vertical. 

Circumscribe, about the 
plan of the pyramid, a rectan¬ 
gle which shall have its sides 
respectively parallel and per¬ 
pendicular to a T-square line. 

The isometric of this 
rectangle can be drawn at 
once with 30-degree lines, as 
shown in Fig. 165, o being 
the same point in both figures. The horizontal projection of point 
3 is found in isometric at 3 A , at the same distance from o as in the 
plan. That is, any dis¬ 
tance which in plan is 
parallel to a side of the 
circumscribing rectangle, 
is shown in isometric in 
its true length and par¬ 
allel to the corresponding 
side of the isometric rec¬ 
tangle. If point 3 were 
on the horizontal plane 
its isometric would be 3 A , 
but the point is at the 
vertical height above H 
given in the elevation; 

hence, lay off above 3 Isometric of a Carpenter’s Bench 

this vertical height, 

obtaining the actual isometric of the point. To locate point 4, 
draw 4 a parallel to the side of the rectangle; then lay off oa 
and a4\ giving what may be called the isometric plan of 4. The 

























122 


MECHANICAL DRAWING 


vertical height taken from the elevation locates the isometric 
of the point. 



Fig. 168. Plan and Elevation of 
Sawhorse 



Fig. 169. Isometric of Fig. 168 


In like manner all the corners of the pyramid, including the 
apex, are located. The rule is, locate first in isometric the horizontal 



projection of a point by one or two 2,0-degree co-ordinates; then ver¬ 
tically above this point, locate its height as taken from the elevation. 
Figs. 166 to 173 give examples of the isometric of various objects. 




































MECHANICAL DRAWING 


123 


Fig. 168 is the plan and elevation, and Fig. 169 the isometric, of a 
carpenter’s sawhorse. 



OBLIQUE PROJECTION 

Comparison with Isometric Projection. In oblique projec¬ 
tion, as in isometric, the end sought for is the same—a more or 
less complete representation, in one view, of any object. Oblique 
projection differs from isometric in that one face of the object is 
represented as if parallel to the vertical plane of projection, the 
others inclined to it. Another point of difference is that oblique 
projection cannot be deduced from 
orthographic projection, as is iso¬ 
metric. 

Characteristics of Method. In 

oblique projection all lines in the 
front face are shown in their true 
lengths and in their true relation to 
one another, and lines which are per¬ 
pendicular to this front face are Fi e- 174 - 0bli< g| of Cube at 30 
shown in their true lengths at any 

angle that may be desired for any particular case. Lines not in the 
plane of the front face nor perpendicular to it must be determined by 
co-ordinates, as in isometric. It will be seen at once that this system 














124 


MECHANICAL DRAWING 


possesses some advantages over the isometric, as, for instance, in the 
representation of circles, as any circle or curve in the front face is 
actually drawn as such. Fig. 174, Fig. 175, and Fig. 176 show a cube 
in oblique projection with the 30-degree, 45-degree, and 60-degree 

slant, respectively. Fig. 177 shows 
a hollow cylinder in oblique pro¬ 
jection. Figs 178, 179, 180, 182 
are other examples of oblique pro¬ 
jections. Fig. 180 is a crank arm. 

The method of using co-ordi¬ 
nates for lines of which the true 
lengths are not shown, is illustrated 
by Figs 181 and 182. Fig. 182 
represents the oblique projection of 
the two joists shown in plan and 
elevation in Fig. 181. The dotted 
lines in the elevation, Fig. 181, show the heights of the corners 
above the horizontal stick. The feet of these perpendiculars give 
the horizontal distances of the top corners from the end of the 
horizontal piece. 

In Fig. 182 lay off from the upper right-hand corner of the front 
end a distance equal to the distance between the front edge of the 



Fig. 175. Oblique View of Cube at 45 
Degrees 




Fig. 177. Oblique View of Hollow Cylinder 


inclined piece and the front edge of the bottom piece, Fig. 181. 
From this point draw a dotted line parallel to the length. The 
horizontal distances from the upper left corner to the dotted perpen¬ 
dicular are then marked off on this line. From these points verticals 














MECHANICAL DRAWING 


125 


are drawn, and made equal in length to the dotted perpendiculars 
of Fig. 181, thus locating two corners of the end. 



Fig. 179. Oblique View of Cylinder 



Fig. 178. Oblique View of a Miter Joint 







1 

1 

! 































126 


MECHANICAL DRAWING 


LINE SHADING 



Object of Line Shading. In finely finished drawings it is fre¬ 
quently desirable to make the various parts more readily seen by 
showing the graduations of light and shade on the 
curved surfaces. This is especially true of such sur¬ 
faces as cylinders, cones, and spheres. The effect is 
obtained by drawing a series of parallel or converg¬ 
ing lines on the surface at varying distances from 
one another. Sometimes draftsmen, themselves, 
vary the width of the lines. These lines are 
farther apart on the lighter portion of the sur¬ 
face, and closer together and heavier on the darker 
part. 

Fig. 183 shows a cylinder with elements drawn 
on the surface equally spaced on the plan. On 
account of the curvature of the surface, however, 
the elements are not equally spaced on the eleva¬ 
tion, in order to give the effect of the graduations of 
light on the curved surface. The result is that 
in drawing the elevation of the cylinder, the dis¬ 
tances between the elements are made gradually less from the center 
toward each side, thus giving a correct representation of the con¬ 
vexity of the cylinder. This effect is intensified by making the 


Fig. 183. Plan and 
Shaded Elevation 
of Cylinder 


Fig. 184. Shaded 
Vertical Cylinder 



Fig. 185. Shaded Horizontal 
Cylinder 


Fig. 186. Shaded Section 
of Hollow Cylinder 


outside elements heavier as well as closer together, as shown in 
Figs. 184 to 190. Concavity is shown in the same manner, the 


















































MECHANICAL DRAWING 


127 


heavy shading always appearing on the left to indicate the deeper 
shadow, Figs. 186 and 188. 

Fig. 184 is a cylinder showing the heaviest shade at the right, 
a method often used. Considerable practice is necessary to obtain 
good results; but in this, as in other portions of mechanical drawing, 
repetition is unavoidable. Fig. 185 represents a cylinder in a hori- 




Fig. 187. Shaded Elbow Joint Fig. 188. Shaded Section of Hollow Sphere 

zontal position, and Fig. 186 represents a section of a hollow vertical 
cylinder. Figs. 187 to 190 give other examples of familiar objects. 



Fig. 189. Shaded Sphere 



Fig. 190. Shaded Cone 


In the elevation of the cone shown in Fig. 190 the shade lines 
should diminish in weight as they approach the apex. Unless this is 
done it will be difficult to avoid the formation of a blot at that point. 




















128 


MECHANICAL DRAWING 


LETTERING 

Types of Lettering. In the early part of this course, the inclined 
Gothic letter was described, and the alphabet given. The Roman, 
Gothic, and block letters are perhaps the most used for titles. These 
letters, being of comparatively large size, are generally made 
mechanically; that is, drawing instruments are used in their con¬ 
struction. In order that the letters may appear of the same height, 
some of them, owing to their shape, must be made a little higher 
than the others. This is the case with the letters curved at the top 
and bottom, such as C, O, S, etc., as shown somewhat exaggerated 
in Fig. 191. Also, the letter A should extend a little above, and V 
a little below, the guide lines, because if made of the same height 
as the others they will appear shorter. This is true of all capitals, 
whether of Roman, Gothic, or other alphabets. In the block letter, 
however, they are frequently all of the same size. 

Size of Letters. There is no absolute size or proportion of 
letters, as the dimensions are regulated by the amount of space 
in which the letters are to be placed, the size of the drawing, the effect 
desired, etc. In some cases letters are made so that the height 
is greater than the width, and sometimes the reverse; sometimes 
the height and width are the same. This last proportion is the 
most common. Certain relations of width, however, should be 
observed. Thus, in whatever style of alphabet used, the W should 
be the widest letter; J the narrowest, M and T the next widest 
to W, then A and B. The other letters are of about the same width. 

Vertical Gothic. In the vertical Gothic alphabet, the average 
height is that of B, D, E, F, etc., and the additional height of the 
curved letters and of the A and V is very slight. The horizontal 
cross lines of such letters as E, F, H, etc., are slightly above the 
center; those of A, G, and P slightly below. 

Inclined Gothic. For the inclined letters, Fig. 192, 60 degrees 
is a convenient angle, although they may be at any other angle 
suited to the convenience or fancy of the draftsman. Many drafts¬ 
men use an angle of about 70 degrees. 

Roman. The letters of the Roman alphabet, whether vertical, 
Fig. 193, or inclined, Fig. 194, are quite ornamental in effect if well 
made, the inclined Roman being a particularly attractive letter, 


MECHANICAL DRAWING 


129 



Fig. 192. Inclined Gothic Letters and Figures 





ABCDEFGHIJKLMN 5 



Fig. 194. Inclined Roman Letters and Figures 



MECHANICAL DRAWING 


131 


although rather difficult to make. The block letter, Fig. 195, is 
made on the same general plan as the Gothic, but much heavier. 
Small squares are taken as the unit of measurement, as shown. 
The use of this letter is not advocated for general work, although 





if made merely in outline the effect is pleasing. The styles of 
numbers, corresponding with the alphabets of capitals given here, 
are also inserted. When a fraction, such as 2f is to be made, the 
proportion should be about as shown. For small letters, usually 

abcdefghijklmn 

opqrstuvwxyz 

Fig. 196. Vertical Gothic Lower-Case Letters 


called lower-case letters, the height may be made about two-thirds 
that of the capitals. This proportion, however, varies in special 
cases. 

Lower-Case Letters. The principal lower-case letters in general 
use among draftsmen are shown in Figs. 196, 197, 198, and 199. 













































































































































































































132 


MECHANICAL DRAWING 


The Gothic letters shown in Figs 196 and 197 are much easier to 
make than the Roman letters in Figs. 198 and 199. These letters, 

abcdefgh/jk/mr? 
opqrs tuvwjcjsz 

Fig. 197. Inclined Gothic Lower-Case Letters 

however, do not give as finished an appearance as the Roman. As j 
has already been stated in Mechanical Drawing, Part I, the inclined 
letter is easier to make because slight errors are not so apparent. 

abcdefghijklmn 

opqrstuvwxyz 

Fig. 198. Vertical Roman Lower-Case Letters 

Spacing. One of the most important points to be remembered ! 
in lettering is the spacing. If the letters are finely executed but 

abcdefghijklmn 
op qr'stuvwxyz 

Fig. 199. Inclined Roman Lower-Case Letters 

poorly spaced, the effect is not good. To space letters correctly 
and rapidly requires considerable experience; and rules are of little 

TECHNICALITY 

Fig. 200. Sample of Letter Spacing 

value on account of the many combinations in which letters are 
found. A few directions, however, may be found helpful. For 



MECHANICAL DRAWING 


133 


instance, take the word TECHNICALITY, Fig. 200. If all the 
spaces were made equal, the space between the L and the I would 
appear to be too great, and the same would apply to the space 
between the I and the T. The space between the H and the N 
and that between the N and the I would be insufficient. Usually, 
when the vertical side of one letter is followed by the vertical side 
of another, as in H E, H B, I R, etc., the maximum space should 
be allowed. Where T and A come together the least space is given, 
for in this case the top of the T frequently extends over the bottom 
of the A. In general, the spacing should be such that a uniform 
appearance is obtained. For the distances between words in a 
sentence, a space of about 1| the width of the average letter may 
be used. The space, however, depends largely upon the desired 
effect. 

Penciling before Inking. For large titles, such as those placed 
on charts, maps, and some large working drawings, the letters 
should be penciled before inking. If the height is made equal to 
the width, considerable time and labor will be saved in laying out 
the work. This is especially true with such Gothic letters as O, 
Q, C, etc., as these letters may then be made with compasses. If 
the letters are of sufficient size, the outlines may be drawn with the 
ruling pen or compasses, and the spaces between filled in with a 
fine brush. 

Titles for Working Drawings. The titles for working drawings 
are generally placed in the lower right-hand corner. Usually a 
draftsman has his choice of letters, mainly because after he has 
become used to making one style he can do it rapidly and accurately. 
However, in some drafting rooms the head draftsman decides what 
lettering should be used. In making these titles, the different 
alphabets are selected to give the best results without spending 
too much time. In most work the letters are made in straight 
lines, although frequently a portion of the title is found lettered 
on an arc of a circle. 

In Fig. 201 is shown a title having the words CONNECTING 
ROD lettered on an arc of a circle. To do this work requires con¬ 
siderable patience and practice. First, draw the vertical center 
line as shown at C in Fig. 201, then, draw horizontal lines for the 
horizontal letters. The radii of the arcs depend upon the general 




134 


MECHANICAL DRAWING 


arrangement of the entire title, and this is a matter of taste. The 
difference between the arcs should equal the height of the letters. 
After the arc is drawn, the letters should be sketched in pencil to 
find their approximate positions. After this is done, draw radial 
lines from the center of the letters to the center of the arcs. These 



BEAM ENGINE 

Fig. 201. Sample Title 


lines will be the centers of the letters, as shown at A, B, D, and E . 
The vertical lines of the letters should not radiate from the center 
of the arc, but should be parallel to the center lines already drawn; 
otherwise the letters will appear distorted. Thus, in the letter N 


SAFETY STOP VALVE 

Fig. 202. Sample Title 

the two verticals are parallel to the line A. The same applies to 
the other letters in the alphabet. In making the curved letters 
such as O and C, the centers of the arcs will fall upon these center 
lines; and if the compasses are used, the lettering is a comparatively 
simple matter. In Fig. 202 is shown another title in which all the 
letters are in horizontal lines. 


PLATES 

Plates IX to XV, inclusive, are to be drawn by the student 
for practice in applying the principles of orthographic projection, 
intersections and developments, isometric and oblique projection, 
and for practice in lettering. These plates are to be made 11 inches 
by 15 inches outside, with a margin of J inch, making the clear 
space for the drawing 10 inches by 14 inches. All the plates are 
to be inked. 




MECHANICAL DRAWING 135 

PLATE IX 

After laying out the border line on the plate, draw a ground 
line horizontally across the upper part of the plate, 3 inches below 
the upper border line. On this ground line six figures, spaced as 
regularly as possible, are to be drawn, as follows: 

1. Draw the projections of a line 1| inches long which is 
parallel to both planes, 1 inch above the horizontal, and J inch 
from the vertical. 

2. Draw the plan and elevation of a line 1| inches long which 
is perpendicular to the horizontal plane and 1 inch from the vertical. 
Lower end of line is | inch above H. 

3. Draw the projections of two intersecting lines: one 2 inches 
long to be parallel to both planes, 1 inch above H, and J inch from 
the vertical; and the other to be oblique to both planes and of any 
desired length. 

Note. The idea for drawing the three figures referred to in 1 , 2, and 3 can 
be obtained from Figs. 104 and 105 in this textbook. 

4. Find the true length of a line whose vertical projection is 
1| inches long, the left end on the grouijd line and inclined at 30 
degrees. The horizontal projection has the left end \ inch from 
F, and the right \\ inches from F. 

5. Find the true length of a line whose horizontal projection 
is 1 inch long, whose right end is | inch above the ground line, and 
inclined at 60 degrees. The vertical projection has the right end 
% inch below the ground line and the left 1 inch. 

6. Find the true length of a line whose projections are per¬ 
pendicular to the ground line. The horizontal projection is 2 inches 
long, the bottom end being \ inch above the ground line. The 
vertical projection is 1 inch long, the top end being | inch below 
the ground line. 

Note. The idea for drawing the figures referred to in 4, 5, and 6 can be 
obtained from Figs. 120 and 121 in this textbook. 

In the lower half of the plate, four more figures are to be drawn, 
also spaced as regularly as possible, so that the finished plate will 
be well balanced: 

7. Draw the plan and elevation of a round bolt with a square 
head. The head is to be uppermost in the elevation. The bolt 



136 


MECHANICAL DRAWING 


is to be 2 inches long and J inch in diameter. The head is to be 
f inch square, J inch thick, and have one face parallel to V . 

8. Draw the plan and elevation of a round bolt having the 
same dimensions as in 7, but with a hexagonal head; the head to 
be uppermost in the elevation, and to be f inch in width between 
faces J inch thick, and to have one face parallel to V. 

9. Draw the plan and elevation of a cylinder, perpendicular 
to H, 2 inches high and 2 inches in diameter, with a hole 1 inch 
in diameter passing vertically completely through it. 

10. Draw the plan, elevation, and end view of a rectangular 
block 6 inches long, 2 inches wide, and 1 inch thick. One of the 
2 inch by 6 inch sides is to be parallel to H. The right end is turned 
down to a cylindrical form 1 inch in length and 1 inch in diameter. 

In all the work of this plate, construction lines should be fine 
dotted lines and should be inked in. 

PLATE X 

The figures on the reproduced Plate X on the opposite page 
give the outline of the work that is to be completed by the 
student. The dimensions given on this plate are to be used in 
working out the problem, but are not to appear on the finished 
plate. The first figure shown represents a rectangular block with a 
rectangular hole cut through from front to back. The other two 
figures represent the same block in different positions. In drawing 
these figures, the student must put in all construction lines in order 
to show how each view is obtained. 

After completing the construction of the views as shown, the 
projection of four holes, ^ inch in diameter each, are to be drawn. 
One hole passes through the center of each end, and one hole through 
the center of each side. All these small holes pass completely 
through to the large hole in the center of the block. Next, put two 
square projecting pieces on the front face of the block, on the center 
line, \ inch from each end. These projecting pieces are to be \ 
inch square and J inch deep. 

The projections of the four small holes and two projecting 
pieces are to be drawn in all views in the conventional manner, 
and the necessary construction lines for this work are to be left 
on the plate and inked in. 



MECHANICAL DRAWING 


137 



rEBRUARY' 90, /S/S. HERBERT CHjANOLER , CH/GAGO, /LL. 

































































138 


MECHANICAL DRAWING 


PLATE XI 

At the left of this plate draw the plan, front and side views 
of the monument shown in elevation on reproduced Plate XI on the 
opposite page. The total height of the monument is 6 inches. 
All four sides are alike except that the width of the base is 2 inches 
and the depth l\ inches, and the width of the body of the monument 
is 1§ inches and the depth 1 inch. The height of the base is J inch, 
of body 3 inches, and the faces just above the base have a slope of 
60 degrees with the horizontal. The width of the ridge at the 
extreme top of the monument is 1 inch. 

The figures for the right side of the plate represent a pen¬ 
tagonal pyramid in three positions. The first position is the pyramid 
with the axis vertical. The height of the pyramid is 2J inches, 
and the diameter of the circle circumscribed about the base 2 \ inches. 
The center of the circle is 6 inches from the left margin and 2\ 
inches below the upper border line. Spaces between figures to 
be \ inch. 

In the second figure the pyramid has been revolved about the 
right-hand corner of the base as an axis, through an angle of 15 
degrees. The axis of the pyramid, shown dot and dash, is therefore 
at 75 degrees. The method of obtaining 75 degrees and 15 degrees 
with the triangles was shown in Part I. From the way in which 
the pyramid has been revolved, all angles with V must remain the 
same as in the first position; hence the vertical projection will be 
the same shape and size as before. All points of the pyramid 
remain the same distance from V. The points on the plan are 
found on T-square lines through the corners of the first plan and 
directly above the points in elevation. In the third position the 
pyramid has been swung around, about a vertical line through the 
apex as axis, through 30 degrees. The angle with the horizontal 
plane remains the same; consequently the plan is the same size 
and shape as in the second position, but at a different angle. Heights 
of all points of the pyramid have not changed this time, and hence 
are projected across from the second elevation. 

PLATE XII 
DEVELOPMENTS 

On this plate draw the developments of a truncated octagonal 
prism, and of a truncated pyramid having a square base. The 




































146 


MECHANICAL DRAWING 


arrangement on the plate is left to the student; but it is suggeste 
that the truncated prism and its development be placed at the left, 



Fig. 203. Plan, Elevation, and Development of an Octagonal Prism 


and that the development of the truncated pyramid be placed under 
the development of the prism; the truncated pyramid may be placed 
at the right. 





Fig. 204. Plan, Elevation, and Deveropment of a Square Pyramid and Cutting Plane 


The prism and its development are shown in Fig. 203. The 
prism is 3 inches high, and the base is inscribed in a circle 2| inches 
in diameter. The plane forming the truncated prism is passed as 
indicated, the distance AB being 1 inch. Ink a sufficient number 
of construction lines to show clearly the method of finding the 
development. 









































MECHANICAL DRAWING 


141 


The pyramid and its development are shown in Fig. 204. Each 
side of the square base is 2 inches, and the altitude is 3f inches. 
The plane forming the truncated pyramid is passed in such a posi¬ 
tion that AB equals If inches, and AC equals 2\ inches. In this 
figure the development may be drawn in any convenient position, 
but in the case of the prism it is better to draw the development 
as shown. Indicate clearly the construction by inking the con¬ 
struction lines. 


PLATE XIII 

ISOMETRIC AND OBLIQUE PROJECTION 

In the upper left quarter of this plate draw the isometric pro¬ 
jection of the block which is shown on reproduced Plate X, page 137, 
taking the dimensions from your finished Plate X. The idea for 
this problem can be obtained by referring to Fig. 158 in this text¬ 
book. 

In the upper right quarter of this plate draw the isometric 
projections of the two round bolts described in 7 and 8 of Plate IX, 
taking dimensions from your finished Plate IX. 

In the lower half of this plate draw, at 45 degrees, the oblique 
projections of the cylinder and the rectangular block, described in 
9. and 10 of Plate IX, taking dimensions from your finished Plate IX. 
The idea for this can be obtained by referring to Figs. 175 and 179 
in this textbook. 

PLATE XIV 

FREE=HAND LETTERING 

On account of the importance of free-hand lettering, the student 
should practice it at every opportunity. For additional practice, 
and to show the improvement made since completing Part I, lay 
out Plate XIV in the same manner as Plate I, and letter all four 
rectangles. Use the same letters and words as in the lower right- 
hand rectangle of Plate I. 


PLATE XV 

LETTERING 

First lay out Plate XV in the same manner as previous plates. 
After drawing the vertical center line, draw light pencil lines as 





PLATE JET 


142 MECHANICAL DRAWING 



MAR. /B./3/6. HERBERT CHANOLER, CH/CAGO, ILL 











MECHANICAL DRAWING 


143 


guide lines for the letters. The height of each line of letters is shown 
on the reproduced plate. The distance between the letters should be 
\ inch in every case. The spacing of the letters is left to the student. 
He may facilitate his work by lettering the words on a separate piece 
of paper, and finding the center by measurement or by doubling the 
paper into two equal parts. The styles of letters shown on the 
reproduced plate should be used. 




















INDEX 

t 








I 

































- 

* 



















' 













INDEX 


Angles. 

measurement of 


A 


B 

Beam compasses. 

Bow pen and bow pencil. 


C 

Circles. 

Compasses. 

Cones. 

Conic sections. 

ellipse. 

hyperbola. 

parabola.. 

rectangular hyperbola. 

Cycloidal curves. 

cycloid. 

epicycloid. 

hypocycloid. 

Cylinders. 


D 

Dividers. 

“ Don’ts” in drafting work. 

Drawing board. 

Drawing instruments, how to hold. 

Drawing paper... 

Drawing pen. 


E 


Ellipse. 
Erasers 


G 

Geometrical definitions. 

angles. 

circles. 

cones. 

cylinders. 

fines. 

polygons. 

polyhedrons. 

solids. 


PAGE 

. 42 
. 46 


16 

13 


45 

10 

49 

51 

51 

52 

52 

53 
53 

53 

54 
54 
49 


12 

25 

2 

22 

1 

13 


51 

4 


41 

42 
45 
49 
49 

41 

42 
47 
47 




































INDEX 

Geographical definitions (continued) page 

spheres. 50 

surfaces. 52 

Geometrical problems. 55 

H 

Hyperbola. 52 

I 

Ink. 14 

Instruments and materials. 1 

beam compasses. 16 

bow pen and bow pencil. 13 

compasses. 10 

dividers. 12 

drawing board. 2 

drawing paper. 1 

drawing pen. 13 

erasers. 4 

ink. 14 

irregular curve. 16 

pencils... 3 

protractor. 15 

scales. 15 

T-square. 4 

thumb tacks. 3 

triangles. 6 

Intersections.:. 98 

planes with cones or cylinders. 103 

planes with planes. 98 

Involute curves. 54 

Irregular curve. 16 

Isometric projection. 113 

applications of. 116 

characteristics of. 116 

isometric of cube. 113 

L 

Lettering.17 } 128 

forming. 17 

inking. i8 

penciling before inking. I 33 

size of. 128 

inclined. 128 

lower case. 131 

Roman. 128 

vertical Gothic. 128 

spacing. 18 

style. 19 

types of. i 28 

working drawings, titles for. I 33 


















































INDEX 


Line problems (preliminary). 

inking. 

penciling. . . 

Line shading. 

Lines. 

true length of. 

by revolving horizontal projection. 

by revolving vertical projection. 

M 

Mechanical drawing. 

conic sections. 

geometrical definitions. 

geometrical problems. 

“don’ts” in drafting work. 

drawing instruments, how to hold. 

instruments and materials. 

intersections. 

isometric projection. 

lettering. 

fine problems (preliminary). 

fine shading. 

fines, true length of. 

objects, representation of. 

objects, rotating and inclining of. 

oblique projection. 

odontoidal curves. 

plates... 

projections. 

surfaces, development. 

0 

Objects, representation of. 

rectangular prism or block. 

triangular block with square hole. 

triangular prism or block. 

Objects, rotating and inclining of. 

cylinder greatly inclined to horizontal plane 
cylinder in inclined position to horizontal plane 

method of rotating. 

pyramid. 

Oblique projection... 

characteristics of method. 

comparison with isometric projection. 

Odontoidal curves.-. 

cycloidal curves. 

involute curves.•. 

Orthographic projections. 

comparison of third- and first-angle projection. 

first-angle projection. 

third-angle projection.. 


TAGE 
. 26 
. 27 
. 27 
. 126 
. 41 
. 87 
. 88 
. 88 


.1-143 

. 51 

. 41 

. 55 

. 25 

. 22 

. 1 

. 98 

. 113 

.17, 128 

./. 26 

. 126 

. 87 

. 8$ 

. 90 

. 123 

. 53 

29-38; 55-71; 134-143 

. 73 

. 106 


89 

89 

90 

89 

90 
95 
92 

90 

91 
123 
123 
123 

53 

53 

54 

73 
75 
75 

74 



















































INDEX 


P 

Parabola. 

Pencils...... 

Plates. 

Polygons. 

quadrilaterals. 

triangles. 

Polyhedrons. 

Projections. 

drawing projection on paper. 

ground line. 

lines. 

methods. 

orthographic. 

practical problems in. 

rules of... 

typical examples. 

Protractor. 


PAGE 

. 52 

. 3 

29-38; 55-71; 134-143 

. 42 

. 44 

. 43 

. 47 

. 73 

. 79 

. 80 

. 80 

. 76 

. 73 

. 83 

. 81 

. 82 

. 15 


R 

Rectangular hyperbola. 53 


S 

Scales. 

Solids. 

cones. 

cylinders. 

polyhedrons. 

spheres. 

Surfaces. 

definition. 

development. 

cone. 

general details. 

rectangular prism. 

regular triangular pyramid. 

right cone. 

right cyfinder. 

truncated circular cylinder. 


T 

T-square. 

Thumb tacks. 

Triangles. 


15 

47 

49 

49 
47 

50 
42 
42 

106 

109 
106 
108 

110 
108 
107 
111 


4 

3 

6 


67 6 










































































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